They never wanted to trade him.
When Adam Lind said something negative about the organization, he was traded days later. When Navarro publicly asked to be traded, they kept him and play him at DH and catcher despite taking playing time away from a much better player.
I have no doubt that no other team wanted him, especially if AA wanted actual talent in return, but if they wanted to dump him he would have been gone already. AA deserves all the blame on this one. I think so little of Gibbons that I'm not even going to blame him for doing stupid things. Take Navarro away from the roster and Gibbons would be forced to play the better players. AA keeping Navarro for as long as he has is the reason for this.