EXCLUSIVE

Amber Heard -- who's in the throes of a divorce with Johnny Depp -- is spending a lot of time with a guy who makes Johnny look like a pauper -- billionaire extraordinaire Elon Musk ... TMZ has learned.

Our sources say Amber has known the Tesla inventor for several years, but in the last few months they've been spending a lot of time together.

Just last weekend Amber and her sister were hanging out in Elon's hotel bungalow in Miami. We're told she had a 1-on-1 dinner at his L.A. house 2 weeks ago. We're told she recently went to Elon's L.A. area office to spend time with him. And we're told he's paid several visits to her home.

No one in Amber's camp is calling it "dating," but we're told the amount of time they spend together has definitely increased.