I think its a tough sell, but it is a possibility. It all depends on how the landscape looks when they find out the new CBA, but if Danny can convince Davis that his best way to get paid is to play one more year here (and play better down the stretch this time), I think it could happen.
Davis certainly did not finish off the year strong, and perhaps teams might shy away from giving him the money he wants this summer. The key is going to be convincing him that he can showcase himself better on the C's, going deep into the playoffs, but with few minutes, than on a team where he might have a larger role, but they don't get the publicity.