A guy who puts a NO trade clause in his contract probably shouldn't be put in this position at all, since the contract pretty much clearly stated he will honor his part of the contract until it's done, and the team who presented him this contract should also honor their end. Now the team comes to him, expects him to uproot his life and follow their orders or feel the wrath from the team and the fanbase if he elects to enforce the NTC. Not sure why he has to be subjected to similar frustration from the team that is trying to trade for him, also.
To me, he ought to be able to take as long as he wants.