I have no strong feelings about any name out there other than Jay Wright or Billy Donovan, but I don't see them being realistic options. I would probably be most fine with Bruce Pearl, even though he hasn't had a load of March success.
If I had to guess, I don't think Calipari will be back, but neither do I think he will be fired. I think Barnhart has the leverage between the two and that he'll use it. He won't fire Cal, but I think he's going to communicate to him that he has the money to buy him out now or in the future. Basically let it be known that he's replaceable and he will not have full control next season. Then the ball will be left in Calipari's court, and the two sides will reach an agreement and Cal leaves.
It's to no one's benefit for Calipari to coach at UK next season. And I don't think he will.