Ken Rosenthal of FOXSports.com writes that free agent Hank Blalock is the next left-handed hitter on the free-agent “pecking order.”

The Cleveland Indians signed first baseman Russell Branyan to a one-year, $2 million deal earlier today. The Tampa Bay Rays were known to be pursuing the left-handed hitting Branyan. Rosenthal suggests that the Rays could be in the picture for Blalock, but the team will be limited by roster space. Rosenthal says the Rays would need to carry 11 pitcher or one less utility man of they signed Blalock.

Blalock, 29, hit 25 home runs in 2009 for the Texas Rangers, but had a .277 on-base percentage, a very unattractive statistic for teams needing a left-handed hitter. You can see Blalock’s contract history and statistics here.