The actor and actress are rumoured to be dating following Depp's split from Vanessa Paradis after 14 years together and the end of Heard's romance with artist van Ree.
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© PA Images / Joel Ryan/AP
A source told Now that, when the Drive Angry star met up with her ex in LA two weeks ago, van Ree said she was "happy" about Heard growing close to Depp.
She has also apparently told friends: "I give them my blessing."
Paradis is said to have branded Heard a "man-stealing, two-bit nobody".
It has also been suggested that Depp may pay Paradis up to £100 million ($156m) in an out-of-court settlement.
Photo gallery - big celebrity break-ups of 2012:
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