According to Johnny Damon he essentially reached out to Brian Cashman and the Yankees and offered to play in New York. He wanted to be a Yankee again so bad that he was willing to accept "whatever [the Yankees] want to pay him."
Brian Cashman supposedly gave him some pretty thin answers about Ibanez being a better fit. That's kind of bullshit because Ibanez sucks at least as much as Damon, and probably more.
I can, however, understand the idea of not wanting to bring Damon back. After all if Ibanez sucks until July the Yankees can always go out and acquire a slugging left handed DH via trade. It's easy enough to cut Ibanez. He isn't getting paid very much and the fans and players have no particular attachment to him. However, cutting Damon mid-season would be much more painful for an organization and a fan base that remembers him playing his heart out for the Yankees and winning a world series here. Even if he did happen to throw like a little girl.