Chloë, 17, and Brooklyn, 15, were photographed together during arrivals at Sunday night's Teen Choice Awards – though the couple didn't walk the carpet together.
The If I Stay actress spoke about their skateboarding dates in Company magazine's September issue, and a source told PEOPLE the son of British superstars Victoria and David Beckham is "totally smitten."
The teens have also been spending time together at Soul Cycle spin classes in Brentwood, California.
"Brooklyn is always chaperoned by one of his parents," a source told PEOPLE last week. "But both David and Victoria must be okay with Chloë, because they will chat briefly with her and then leave them alone."