The 26-year-old actress and the director, who is 21 years her senior, have set tongues wagging after they were spotted on a string of low-key dates in Los Angeles recently, reported Female First.
The pair reportedly struck up a romance after they bonded over their new film, which is yet to be given a name and also stars Javier Bardem and Michelle Pfeiffer, over the summer.
"Jennifer and Darren have tried to keep things low-key and under wraps but they are really into each other. Recently Jennifer was working on a gruelling project and she relied on Darren for support and they were in constant contact. It seemed to show they were the real deal," a source said.
The "Joy" previously dated Coldplay's Chris Martin and Nicholas Hoult.
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