I will admit this is purely speculation, but I don't think it's out of the realm of possibility.
Here's what we know - Montero's defense behind the plate has always gotten mixed reviews from scouts. Publicly, the Yankees still consider him to be a catcher, but privately, what if they're not so optimistic?
This is critical, because if the Yankees don't see Montero as even a part-time catcher in the big leagues, where else is he going to play for them? They have long-term contracts and/or better players at first base, left field, and right field, and with an older roster, it makes no sense to carry a rookie DH.
If this is the conclusion that the Yankees brass has come to - and all I'm suggesting is that it's plausible - then it doesn't matter how good a hitter Montero is, his only value to Yankees is as trade bait, and the sooner the better.
At the same time, if they're going to get Cliff Lee one way or the other, why not trade for him now, keep the draft picks you would have had to surrender, and trade Javier Vazquez for prospects? From an organizational standpoint, the sum of those parts may have more practical value than a hitting prospect who has nowhere to play, and it gives them an absurdly good rotation for this year's playoff push.
If the Yankees are pessimistic about Montero behind the plate, this actually makes a lot of sense. We'll see what happens.