It's gotta be someone who can do dirty work and play defense on Centers, because otherwise Horford is the only post defender on the roster. Because of Horford's versatility, it could be a center also.
Ideally it's a high IQ, versatile big who can shoot, pass, and defend multiple positions. Also, it'd be nice if he could put some points on the board.
On top of all this, it'd be ideal if we didn't give up a ton of assets, because even if we get a guy like this, it is largely a lateral move that doesn't vault us into contention. We don't want to be like the Wizards and their constant short-term moves.