According to MLB Trade Rumors, each of the following three pitchers have cleared waivers and are therefore eligible to be dealt. The numbers presented represent their numbers against left-handed batters, as the Yankees have enough talented righties to allow Girardi to leverage Logan and another lefty to the best of their abilities.
Bill Bray, Reds
2011 - .195/.273/.286, 9 BB, 21 K
Career - .231/.309/.344, 35 BB, 72 K
In terms of salary, Bray is the cheapest of the bunch - but I imagine the Reds seeking a bit more than a middling prospect as he has an arbitration year remaining. Put simply, they aren't faced with dealing him or letting him walk for nothing ... and I could see them getting a bit more value at next year's trade deadline.
Mike Gonzalez, Orioles
2011 - .207/.250/.322, 4 BB, 26 K
Career - .212/.279/.339, 39 BB, 150 K
Gonzalez is the most expensive of the trio, and a free agent at year's end. The Orioles have no reason to hold onto him, but I would be shocked if they would hand him to the Yankees - particularly following the spat with the rescheduling of this past weekend's games.
Tom Gorzelanny, Nationals
2011 - .171/.229/.316, 4 BB, 23 K
Career - .236/.301/.368, 44 BB, 134 K
Gorzelanny will be arbitration eligible at the end of this year, with a year of team control remaining in 2013 as well (according to Baseball Reference). For that reason, I don't see the Nationals flipping him for nothing - but I do think that he's a worthwhile option as an affordable option that could also work well as a swingman.
I would be satisfied with any of the three, to be perfectly honest. My personal choice would be ... whomever could be acquired for the least.