Brooklyn Beckham 'Smitten' by Chloë Grace Moretz, Source Says

Brooklyn Beckham 'Smitten' by Chloë Grace Moretz, Source Says
Brooklyn Beckham and Chloë Grace Moretz
David M. Benett/Getty; Ari Perilstein/Getty

08/09/2014 AT 09:35 AM EDT

Nice guys finish ... as Chloë Grace Moretz's boyfriend?

Brooklyn Beckham, 15, is "totally smitten" by the If I Stay actress, 17, a source tells PEOPLE. The teens have been seen skateboarding and enjoying friendly competitions at Soul Cycle in Brentwood, California.

"Brooklyn is very sweet and shy, a really nice boy," says the source. "Chloë is more sophisticated." So his parents, David and Victoria Beckham, have been "naturally protective" of Brooklyn, but met Moretz at their spinning classes and allow the teens to enjoy their time together.

Moretz opened up about hanging out with Brooklyn in Company magazine's September issue.

"Who's better? I don't know! I mean, he had a pretty small skateboard, and I had more of a long board," Moretz said. "I think he's a risk taker, like a typical guy, weaving in and out of people. I'm a 'safety boarder.' I don't want to break any bones!"

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