Martinez has been losing playing time for STL and reports are that they may trade him. I think he would certainly be an interesting piece to add for the Rays where he will be under team control for 4 more seasons and could DH since he is not very good at fielding.
The question then becomes, what would be the cost of acquisition. I saw a report stating they could move him for a lefty reliever or lefty hitting position player. A quick glance at their 40 man roster shows them with only Dexter Fowler, a switch hitter, that can bat from the left side of the plate and strangely they do not have a single left handed hitting outfielder in AAA or AA that "you should know" per Roster Resource.
The Rays have lots of left handed hitting outfielders within their system, so would a trade of Mallex Smith for Jose Martinez make sense? He has the same amount of control remaining and would give them a defensive boost in the outfield and speed on the bases.
For Tampa Bay, this still leaves many players capable of playing the OF and bat left handed:
MLB - KK, Bauers, Wendle
AAA - McCarthy, B.Lowe, J. Williams, Wong, Micah Johnson, Velazquez
AA - Dalton Kelly, Nathan Lukes, Ryan Boldt
Mallex Smith for Jose Martinez, who says no?