Chloe Grace Moretz and Brooklyn Beckham are "very competitive."
The 17-year-old 'Carrie' actress and the 15-year-old British model, who recently started dating, have been enjoying low key dates at popular spinning gym Soul Cycle in Brentwood, Los Angeles over the summer.
A source told PEOPLE.com: "They cycle next to each other and are very cute. Always look to be cheering each other on with smiles. They also both seem very competitive, but in a fun way."
Despite being fans of the actress, Brooklyn's parents, David and Victoria Beckham, always supervise his dates with the 'Kick-Ass' beauty.
The insider said: "Brooklyn is always chaperoned by one of his parents. But both David and Victoria must be okay with Chloe, because they will chat briefly with her and then leave them alone."
The couple started dating three months after after being introduced at Paris Fashion Week by mutual friends.
Brooklyn has been photographed leaving Soul Cycle classes regularly, where he often out-performs retired footballer David.
Another source said: "He comes in with his parents - one or the other. He's adorable. You usually see him come in with his dad, who is obviously gorgeous, and all the women in the class just stare.
"You'd think David would be awesome at it, but in fact, Brooklyn just crushes it.
"[Brooklyn] can do all these amazing moves. He's a natural athlete. You don't know what he's going to do next, but you can tell he's got that Beckham gene."

Ryan Reynolds has been cast to appear in new thriller 'Criminal'.
The Hollywood heartthrob will appear in the new flick from Millennium Films alongside Kevin Costner, Gary Oldman and Tommy Lee Jones.
The film focuses on the secrets and skills of a deceased CIA operative, which are implanted into a prisoner who strives to stop a sinister plot.
'Criminal' is to be directed by Ariel Vromen, who wrote and directed 'The Iceman'.
The script is being penned by Douglas Cook and David Weisberg, while Chris Bender, J.C. Spink, Mark Gill and Matt O'Toole have been named as producers of the film.
Reynolds, 37, is sure to work on his latest role with wife Blake Lively, 26, who told the August issue of Vogue magazine that the couple collaborate on everything.
She said: " If I'm working on a movie, he helps me with my character; I do the same with him."
Lively added: "He's a beautiful writer - he's written a lot of stuff for us. And he's got a great barometer and he knows me, so he will tell me if it's not as good as it can be."

Katie Price has posted an adorable picture of cheating husband Kieran Hayler holding hands with their newborn daughter.
The 36-year-old star, who was left devastated earlier this year after discovering the part-time stripper had been sleeping with two of her friends, took to her YouGossip account on Tuesday afternoon (05.08.14) to share a picture of Kieran and their second child, who was born on Monday (04.08.14).
She captioned the image: "Daddy's little girl :)"
Katie - who also has 11-month-old son Jett with Kieran - gave birth to her fifth child on Monday, two weeks before she was booked in to have a Caesarean.
It is not known whether Kieran was present at the birth but in her last interview before she welcomed the little one into the world she revealed he would be there.
When asked whether he would be at the birth, she told OK! magazine: "Yes. Even if my waters break early then he will be there."
Earlier this year, Katie took to her Twitter account to reveal she was getting a divorce after discovering Kieran had been having a "full blown sexual affair" with her good friend Jane Pountney.
She later found out he had also been cheating on her with her pal Chrissy Thomas, however she has decided to give him another chance and stand by him while he undergoes therapy.
Katie also has children Harvey, 12, from her relationship with Dwight Yorke and Junior, nine and Princess, seven, with ex-husband Peter Andre.

Kristin Chenoweth has called on fans to pray for her after she was struck down with a mystery illness.
The 'Glee' star took to her Twitter account to reveal she was staying positive despite being "unable to move" on Monday (04.08.14) as a result of unknown condition, and she is now awaiting test results to find out what is wrong with her.
She wrote: "Waiting on MRI results. No matter what I will be ok. Thanks everything for praying and sending good vibes. #thinkingpositive (sic)"
On Monday, Kristin wrote: "Back in la. Unable to move. Numbness and tingling in arm. Going to cedars dr tomorrow. Ah anyone who prays please do! (sic)"
The 46-year-old actress was clearly keen to cheer herself up as shortly afterwards she retweeted a fan's message which featured a picture of the star's book, 'A Little Bit Wicked: Life, Love, and Faith', which the supporter had recently bought.
Kristin's latest illness comes after the former 'Pushing Daisies' star revealed in March that she has been suffering from asthma for more than a decade.
She said: "I haven't really discussed the fact that I do suffer from asthma. I kept getting sick and couldn't figure out why I couldn't get my breath... that's kind of my asthma journey, if you will."

Dame Helen Mirren loves getting "a jolly good spanking".
The 69-year-old actress featured in a comedic 'Snow White' parody entitled 'Mirren Mirren on the Wall' on 'The Tonight Show' on Monday evening (04.08.14), in which host Jimmy Fallon asked the star several questions to which the star replied with some saucy answers.
When asked for her opinion on the upcoming '50 Shades of Grey' film, Helen - who has been married to US director Taylor Hackford since 1997 - quipped: "Well, whips and chains are not my style. But who doesn't love a jolly good spanking once in a while?"
To a further question about what she orders at the high street sandwich chain Subway, the Academy Award winner cheekily responded with another innuendo.
She joked: "My motto in life is you can never go wrong, by treating yourself to a nice foot-long."
The 'Calendar Girls' star - who celebrated her birthday last month - appeared alongside 'Avatar' director James Cameron on the show to celebrate its 100th episode.
Elsewhere in the sketch, Helen admitted that she is a fan of cult-film 'Sharknado' and revealed her dream job would be to be a contestant on 'American Ninja Warrior'.

Tamara Ecclestone loves being a "hands-on mum".
The 30-year-old socialite gave birth to daughter Sophia four months ago and she is thoroughly embracing everything that motherhood has thrown at her.
Tamara - who is married to Jay Rutland - said: "I love being a hands-on mum.
"I made a decision to be a mum who'd raise my baby with the support of my family and Jay.
"I was there for the first times Sophia rolled over, smiled and giggled in her sleep. There are times we do have help from the nanny, but they're in the minority."
While Tamara's Formula 1 boss father Bernie Ecclestone is now worth £4.2 billion, she insists he didn't spoil her and sister Petra too much when they were younger, and she intends to follow his example with Sophia.
She added to Mother & Baby magazine: "It's important not to give a child everything they want when they want it - my parents would give us something if we did a chore or walked the dog."
Tamara took to Instagram to tell her fans she had become a mother for the first time in March by posting an adorable snap of her looking lovingly at her newborn daughter from her hospital bed.
She captioned the image: "Welcome to the world Sophia, our beautiful baby girl, born yesterday 6lb 9oz. Proudest day of our lives, never felt love like this. X (sic)"

Kellan Lutz wants Angelina Jolie to star in 'The Expendabelles'.
The 29-year-old actor, who plays John Smilee in 'The Expendables 3', is very excited there is a female version of the action film franchise in the works and he would love to see the 39-year-old actress, Cate Blanchett, Cameron Diaz and Jessica Biel appear in the project.
When asked who he would like to see star in 'The Expendabelles' at the world premiere of 'The Expendables 3' in central London on Monday night (04.08.14), Kellan told BANG Showbiz: "Cate Blanchett, Angelina Jolie, Cameron Diaz, Jessica Biel ... I mean there's just so many, that could be in there."
Kellan got to share the screen with an array of legendary Hollywood actors in 'The Expendables 3', such as Sylvester Stallone, Antonio Banderas, Wesley Snipes, Arnold Schwarzenegger, Mel Gibson, and Harrison Ford, and he particularly liked spending time with Sylvester and Jason Statham.
He added: "I love working with Sly but you know, Wesley Snipes and Antonio Banderas ... they are just freaking studs, like they're very fun to work with, very hilarious and Jason Statham's just a badass so it's very fun to hang out with Transporter and Crank, you know, he's just a dude."
Kellan was joined on the red carpet by a host of his co-stars including Sylvester, Wesley, Antonio and Jason.
Other guests at the premiere included chat show host Jonathan Ross, comedian Jack Whitehall, boxer David Haye and actor Vinnie Jones.

The Earl and Countess of Wessex attended a First World War commemoration service in Guilford last night (04.08.14).
The royal couple joined hundreds of guests at the "solemn" service, which started at 10pm and concluded an hour later, at Guildford Cathedral in Stag Hill to mark 100 years since the Great War began in 1914.
Dianna Gwilliams, the Dean of Guilford, hoped the event was built around respect rather than sadness.
She said during the service: "What is very important about this service is the fact it is remembering the eve of something, so it is a vigil.
"Like that which was felt on the actual eve of war it involves waiting and watching and it is that waiting and watching that reminds us of all that happened.
"What is important about not only this event but those up and down the country is they are nothing about war but about peace and wanting peace and the importance of peace in wars still ongoing."
Edward, 50, concluded the readings by echoing the words of the foreign secretary of the time, Sir Edward Grey, who said: "The lamps are going out all over Europe; we shall not see them lit again in our lifetime."

Cheryl Fernandez-Versini wanted "to go back to the pop route" for her new album.
The 31-year-old singer is set to release her fourth LP 'Only Human' in November and she admits she wanted to include a mixture of genres to put a "fun" spin on the collection.
Speaking to MTV News UK, she said: "The album is the most versatile album I've done so far. There's a lot of flavours on there. I wanted to go back to the pop route and do a lot of pop, there's a bit of RnB on there, a bit of 90s dance vibes, I mean it's just fun, you know it's hopeful, it's up-lifting."
She added: "I just want people to enjoy themselves for an hour... I'm not saving lives, I'm making pop music you know."
Meanwhile, the brunette beauty - who recently got married to her beau Jean-Bernard Fernandez-Versini following a whirlwind romance - wants to drop her surname and be known as "just Cheryl" in her professional work because her fans are struggling to pronounce her marital moniker.
She explained: "It's just Cheryl, keeps everything simple, people seem to be having a hard time so you can just call us Cheryl."

Beyoncé didn't want Nicki Minaj to "hold back" in their new 'Flawless' remix.
The 32-year-old singer wanted the 31-year-old rapper - whose real name is Onika Maraj - to let loose when she recorded her verse for the re-worked track.
Speaking on radio station Hot 97, Nicki said: "A month or two ago, Gee [Roberson] called me when I was on my way to Vegas and said, 'Beyoncé wants you to remix to 'Flawless'.
"After I got proper medical help and started breathing again, I was like, 'What?'
"She sent me a version that she wanted. She told me, 'I want you to be you. I don't want you to hold back.'
"I was actually in New York writing the verse. I recorded the verse in New York and she stopped by the studio. She was such a sweetheart. She was hyping me up, 'Do your thing. Don't hold back. Go in.' "
However, the busty brunette admits she didn't think a collaboration with Beyoncé would ever happen at this stage in her career.
She explained: "I figured that eventually we would do something together. I mean, I'm not gonna lie. Recently I thought it would never happen because I felt like if she was going to ask me, she would have asked."
She added: "I think the stars aligned the right way. We are just in the right places in our careers that it makes sense now."
'Flawless Remix' was released last weekend.

Charlotte Crosby is set to interrupt her ex-boyfriend Gaz Beadle's date with new lover Marnie Simpson when she returns to 'Geordie Shore' tonight (05.08.14).
The loud-mouthed beauty creates an awkward atmosphere when she unexpectedly storms into the intimate candle-lit dinner on the MTV reality show and catches the loved-up pair toasting their new romance.
In tonight's episode, Marnie says: "Charlotte has just walked through the door; this is going to ruin everything.
Gaz adds: "Sh*t. I genuinely cannot believe I've just made a toast to me and Marnie and in walks Charlotte. F**k my life."
However, Marnie is left stunned when a drunk Charlotte approaches her on a night out and tells her she's glad her former flame has found someone he's happy with.
She tells the brunette beauty: "Marnie, I've had a boyfriend for over a year now. Don't you ever think that you getting with Gary would ever hurt me. It makes me happy just to think that finally he's met someone who he doesn't have to sh*g people in front of."
Marnie, who initially thought she was going to have a bust-up with Charlotte, is confused by the stunning star's polite behaviour
She says: "What the hell? Me and Charlotte are actually getting on. This is not what I expected tonight, but I am really happy about it."
'Geordie Shore' continues tonight on MTV at 10pm.

Brian Blessed has revealed he turned down the role of 'Doctor Who'.
The British actor was approached to take on the iconic role in the mid-60s when First Doctor William Hartnell was about to be replaced in the TARDIS.
However, he declined due to other work commitments meaning the BBC went on to cast Patrick Troughton as the Second Doctor.
In an interview with Radio Times magazine, Blessed revealed: "After I was in 'Z Cars', the head of BBC serials took me aside and said, 'We're thinking of having a young Doctor Who and we'd like to cast you'. But it clashed with other things."
When asked what his decision would be now if he was asked to star as the lead in the sci-fi series, he replied: "I'd jump at it!"
Blessed - beloved for his performance in cult sci-fi film 'Flash Gordon' - has some interesting ideas as to who should be cast as the Doctor when Peter Capaldi, who is about to debut in the role in a couple of weeks, decides to exit the TARDIS.
He said: "I think they need to re-examine his surname - 'Who' is very oriental. It's about time they had an Asian actor as the Doctor and a female one."
Blessed, now 77, did eventually appear in a 'Doctor Who' adventure in 1986 playing King Yrcanos in the story 'Mindwarp' - part of the series-long narrative 'The Trial of a Time Lord' - opposite Sixth Doctor Colin Baker.