Teahen hit .271 while connecting on 12 home runs and driving in 50 runs last season. The 28-year-old lefty has spent his entire five-year career with the Royals.
Fields, who was supplanted as the everyday third baseman by Gordon Beckham, also spent time in left field and first base for the White Sox this year. His .222 batting average in 79 games, along with Beckham's stellar rookie year made his move more likely.
Getz, a second baseman, hit .261 in his first full year in the majors and stole 25 bases.
White Sox beat writer Joe Cowley reports there is no comment from the White Sox at this time.