The Rays are still looking for a center fielder, ESPN.com's Jayson Stark reports (Twitter link). However, there's not much out there at this stage in the offseason. Stark wonders if the Rays could be a landing spot for Michael Bourn, the top free agent position player remaining.
Troy Renck of the Denver Post notes that the Rockies are among the many clubs that like Jeremy Hellickson and wonders if the Rays could have interest in Dexter Fowler (Twitter link). As MLBTR's Free Agent Tracker shows, Bourn, Scott Podsednik and Grady Sizemore are the only free agent center fielders still available. Gerardo Parra comes to mind as a trade candidate capable of playing center field.
Desmond Jennings, who played 21 games in center field this past season, would presumably start in center if the Rays don't add another player at that position. If the Rays do acquire a center fielder, Jennings might shift back to left field with Sam Fuld and Brandon Guyer assuming reserve roles. B.J. Upton played center for the Rays for years before signing with Atlanta as a free agent this offseason.