I'm not sure what we should be targetting if we were to deal. MLBTR picked up a Heyman report saying that we still may be hunting White Whale, but I don't see the White Whale as critical to this team this year. I think we are kind of locked in with Morse-Harper-Werth / Moore and LaRoche. As much as we bash the offense, I think we go with what we have the rest of the way.
I don't see Morse or LaRoche being valuable to a rebuilding noncontender who would trade us, say, a Span or Revere. If you are thinking Parra, they have Goldschmidt, Kubel, and Upton in the corners. As for a blocked / redundant CF on a contender (I count any >.500 team as a contender right now), you would have to find one that could use a 1b /dh /lf that does not have a log jam. Maybe TB would move Upton for the ROS in the right package (play the Big Birther in LF, with Jennings and Joyce, DH Morse, and keep Pena implanted at 1st). Luke must find enough of the force to to get healthy again for that to work. Thinking about it, a move for Upton might be the most doable CF move we could make, but it would not be a long term fix, and therefore not the White Whale.
Isn't the more likely move something like a bullpen upgrade (try to improve over Gonzalez and Mattheus?) or a back end of the rotation arm?