The two had a late lunch together on Sunday at Green Lemon -- an awesome Mexican restaurant in Tampa, FL ... right near where the Yankees hold spring training.
We're told the two were there for more than an hour -- and were holding hands and acting couply the entire time. You can see in the pics Anne had her arm around A-Rod while the 2 chowed down.
For the record, 40-year-old A-Rod has reportedly made $342 million playing baseball. 42-year-old Anne (who runs a medical research company) reportedly raked in several billion dollars when she finalized her divorce from Brin in 2015.
So, the question ... who paid for lunch?