Pro Football Talk is reporting, per a "league source," that the main hold up on John Abraham signing with a team is that he is waiting for someone to tell him he can play "60 or more snaps per game." There is no shot that any team out there is going to guarantee him something like that at his age. He is going to be more of a situational player than an every down player wherever he ends up.
That is especially true for the Titans. Kamerion Wimbley and Derrick Morgan were both on the field for a lot of snaps last season. Part of that was because the Titans had absolutely no one behind them, but a big part of it was because they both played really well against the run and the pass.
The Titans also started to use Akeem Ayers at defensive end on passing downs a lot at the end of the season. That worked well, so there is no reason to believe they would want to get away from it in 2013.