Per CBS Sports' Jon Heyman, the White Sox have "checked in" on Arthur Rhodes and expressed interest in Mike Gonzalez. These two left-handed relievers would make sense for a bullpen that, as things stand right now, only has one lefty setup man, with that being Will Ohman.
Rhodes was pretty ineffective in his age 41 season last year and was rocked by both lefties and righties during stops with World Series foes St. Louis and Texas. He posted good seasons from 2008-2010, but given his age, the chances he bounces back seem slim.
Gonzalez makes more sense. His best days (which were very good between Pittsburgh and Atlanta) are probably behind him, although he worked out pretty well as a lefty specialist for Baltimore and Texas last year. Like Ohman, if he's used mainly against lefties, he'll be successful -- in 2011, he had a 276 KBB and allowed seven runs in 28 innings pitched against left-handed batters.
If the Sox do sign either of these relievers, it won't be to make a trade of Matt Thornton more palatable, as MLB Trade Rumors' Tim Dierkes writes. The White Sox have tried to have multiple lefties for setup situations in the past, and right now, they don't have that. What we can infer about Thornton's status from these rumors, though, is that he's pretty well entrenched as the team's Opening Day closer.
Like he was last year, which led the Sox to sign Ohman. Maybe this year it'll lead them to sign Gonzalez.