Johnny Damon has come out and said that he is not the Yankee's choice to be their DH. He was a little disappointed at that fact but, he is as pro as understands that this is a business decision and that he wasn't their first choice.
From a Yankee stand point I wouldn't be attracted to Damon either, because if you ever have to put him in the outfield everybody knows instantly that they can run on his arm. His arm is significantly worse than that of Bernie Williams and that is impressive.
The Yankees will almost certainly now bring in Raul Ibanez to play DH against right handed pitching. He can hit some homers to right but will definitely need to platoon with somebody who hits lefties well like Andruw Jones or the full in DH spot guy like Martin, AROD, or Swisher.