Ramirez, 34, has spent his entire eight-year career with the White Sox after signing as an amateur free agent from Cuba in 2008.
He finished last season with a .249 batting average to go with his 33 doubles, 10 home runs, 62 RBIs and 17 stolen bases in 154 games.
Ramirez is a two-time Silver Slugger award winner and was a finalist for a Gold Glove in 2014. His has hit for a career .273 batting average with 109 home runs, 1,272 hits and 542 RBIs.
The White Sox may be looking for a temporary option at shortstop as they await the major league debut of prospect Tim Anderson, who played in Double A this season.
- Christopher Chavez