Sox manager Ozzie Guillen informed Thome that the team will not be offering him a chance to be included among the team's rotating cast of designated hitters.
General manager Ken Williams gave Guillen the final call on the move, and Guillen decided he couldn't give Thome enough at-bats to justify bringing him back.
"It came down to getting enough at-bats,'' Guillen told the Chicago Sun-Times. "I don't want a season where Jim sits three or four days in a row and the media comes up to him and asks, 'You're not playing ...?' This thing will become a soap opera. It's about at-bats."
Thome joined the White Sox in 2006 and spent nearly four seasons with the club before he was traded to the Los Angeles Dodgers on Aug. 31. The Minnesota Twins are rumored to be interested in the slugger.
Sources close to the situation told ESPNChicago's Bruce Levine that Guillen would only have Thome back as a part-time DH. He plans to use a rotation of Paul Konerko, Andruw Jones, Mark Kotsay and Omar Vizquel in the DH spot.
"I talked to Jim [Sunday] and I made everything clear, how he would have to work with the ballclub," Guillen told the Sun-Times. "[Thome] wouldn't get that many at-bats for the ballclub [and would] play once a week, twice a week. I don't think it was fair for him."
Guillen discussed the possibility of bringing Thome back if they see a need in the lineup in spring training and Thome is still unsigned.
"But hopefully Jim is not waiting that long," Guillen told the Sun-Times. "Hopefully Jim has found a job.''
Thome, who will be 40 in August, has 564 career homers, including 134 in his three-plus seasons with the White Sox. He hit 23 a year ago for Chicago before he was traded to the Dodgers. With Los Angeles, he was 4 for 17 in 17 games.
Guillen said the decision not to bring back Thome -- a fan favorite whose home run was the deciding factor in the 2008 play-in game against the Twins -- was a difficult one.
"It's a tough conversation when you release somebody. We didn't release Jim, we just don't have him back," Guillen said. "He's a friend. He's a respect player. The way we feel about him. It's not easy."
The White Sox also did not re-sign right fielder Jermaine Dye, another longball threat who slumped in the second half last season.
Information from The Associated Press was used in this report.