The 34-year-old Ramirez has played his entire career with Chicago after leaving Cuba and is a .273 hitter with 109 homers and 542 RBIs in eight seasons. He was an AL All-Star in 2014 but batted a career-low .249 this year with 10 homers and 62 RBIs.
Chicago could re-sign Ramirez as a free agent or give playing time to Tyler Saladino, a solid fielder with a questionable bat. Shortstop Tim Anderson, among the team's top prospects, hit .312 at Double-A Birmingham this year.
The White Sox also selected the contract of left-handed pitcher Zach Phillips from Triple-A Charlotte, where he went 1-1 with a 3.13 ERA and 12 saves in 46 relief appearances this year. He is 0-1 with a 3.45 ERA in 19 relief appearances with Baltimore (2011-12) and Miami (2013). He was signed by the White Sox last December.