The couple, who have yet to confirm or deny a relationship, were seen holding hands as they left The Rolling Stones' backstage party at the Los Angeles' Echoplex this weekend. Depp, 49, and Heard, 27, kept their head down low as they quietly exited the venue before driving away in the same car.
Previously, Heard was linked to Tasya van Ree and French model Marie de Villepin.
Meanwhile, Depp and Paradis had been in together since 1998 before calling it quits last June. They have two children together: Lily-Rose and Jack.