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Seattle is talking to the Rays about Michael Morse, according to Jon Heyman of CBS sports (h/t Ben Tumbling).
Morse would be an upgrade for the Rays only as a designated hitter against left handed pitching. Over his career he's posted a 136 wRC+ against lefties, and this season he's posted a 160 wRC+ (in only 69 at bats). Luke Scott, the current DH, has posted a 120 wRC+ against lefties this season (71 at bats), but has been a bit below average against them over the course of his career.
If Morse were to arrive in Tampa Bay, it would likely be in a deal that sends Sean Rodriguez to Seattle. Ben Zobrist (switch hitter) and Kelly Johnson (platoon neutral) have made S-Rod somewhat redundant since the righty Wil Myers is now locked into right field, and there's always the very similar Ryan Roberts waiting in the minors.
Still, this is the Rays, and I very much doubt anything happens.
UPDATE: 2:25 PM
Marc Topkin has reported to twitter on two occasions today that Ryan Roberts may be on his way to the Trop:
Sounds like Ryan Roberts is here in St. Pete, or on the way. Kind of a taxi squad situation if a #Rays move (DL or otherwise) is made
— Marc Topkin (@TBTimes_Rays) July 31, 2013
A possible injury could be Ben Zobrist, who has fouled a couple pitches off himself lately and may have hurt his ankle doing so last night, but nothing is confirmed.
The "otherwise" would presumably be due to the trade of a player on the 25-man roster.