Moretz, 17, and the aspiring model, 15, were introduced a couple of months ago through a mutual friend at SoulCycle in Santa Monica, Calif., where Brooklyn often works out with his famous father.
They've "gone on a couple dates and are seeing where it goes," the insider tells Us. "They were each others' crush." A second source notes that the couple have since returned to SoulCycle to take classes together.
The pair have tried to take advantage of Brooklyn's time in L.A. since exchanging information—he's currently back in London finishing school. Some of their other activities have included spending time at the beach, skateboarding, and catching a movie at the Third Street Promenade downtown.
"They don't drive, so they had to be chaperoned around," according to the first source. "It was very cute." Up next, Moretz is planning to take Beckham to her If I Stay film premiere.
Despite getting to know Beckham, Moretz told Flare magazine last month that she doesn't want her life to be all about relationships. "That's not my style," she said. "It's a tough age to fall in love: people change so quickly. I don't want to have to feel like I have to watch my step, 'cause I'm 17 and I shouldn't have to."
Her view is something she's shared with close friends. "I'm like, Dude, you're wasting away your entire high-school years, and now you're going to waste away your college years," she told the mag. "You're going to spend your entire life in a relationship and then you're going to get married...and then you're dead!"