Now that Jesus Montero has been traded, the Yankees probably will obtain a DH. The most prominent names rumored have been Carlos Pena and Carlos Lee, but I am a tad skeptical. This is because given A-Rod's recent hip and knee issues and his age, it would be wise of the Yankees to have A-Rod DH at least twice per week, in order to keep him in the lineup both in 2012 and in future years. In addition, Girardi seems inclined to use the DH slot to give regulars a half-day off, so I would expect the "regular" DH to play 3-4 games a week at that slot. It seems unlikely that Pena and Lee are good matches for that type of role.
Posada is another matter, he proved last year that he has accepted a limited role. But you may ask, "didn't Posada just retire?"