The 17-year-old actress has reportedly been in a relationship with the 15-year-old model, who is the eldest son of Victoria and David Beckham, for three months, after being introduced to him at Paris Fashion Week.
A source told the Daily Mirror newspaper: “They were introduced through mutual friends, and have the same social circle back in Los Angeles.
“They speak all the time and enjoy hanging out together, just doing what teenagers do.”
The couple were first spotted skateboarding together in Santa Monica in June and Brooklyn’s famous parents are said to be huge fans of the Kick-Ass beauty.
The insider said: “Both David and Victoria have given them their blessing.”
But their romance is not thought to be serious, as Brooklyn lives in London and Chloë recently insisted she is too young to be in a committed relationship.
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.”
The Carrie star, who is close friends with Taylor Swift, also isn’t happy that so many of her pals are already in long-term romances.
She told the September issue of Flare magazine: “I’m like, ‘Dude, you’re wasting away your entire high-school years, and now you’re going to waste away your college years. You’re going to spend your entire life in a relationship and then you’re going to get married…and then you’re dead! So you lived your life in a relationship!’ That’s not my style.”
Chloe previously posted this pic on Instagram of her skateboarding with Brooklyn: