"Word is they've quietly gone out a bunch of times since last year, and the out-of-left-field relationship is sure to shock everyone, especially Jen," a source tells the US publication.
"Pals think they're really starting to develop feelings for each other."
According to Life & Style, the "spark was instant."
Life & Style adds that Jolie arranged for the pair to meet up at Justin's favourite NYC restaurant in August under the pretence of talking about a movie role.
What ensued wasn't what either were expecting, the publication notes.
Angelina and Justin found they actually have a lot in common.
"Since that night, their relationship has only grown in momentum and intensity," claims a source, adding that at this point "friends wouldn't be surprised if they're sending steamy texts and having secret sleepovers."
For now, they've managed to fly under the radar.
"It's the best-kept secret," an insider says, "but its not like Ange is worried about the romance getting out."
The new romance is "Jen's worst nightmare".
"I don't care how much chemistry Ange and Justin have, what they're doing to Jen is just plain cruel," says a friend.
Jen, Justin and Angelina are yet to respond to Life & Style's report.