His agent, Craig Landis, said he'll shut down Putz's side sessions after Friday until the early part of January.
The Sox and Cubs are among 12 teams interested in Putz. The South Siders have been the most active team for the former Mariners closer and Mets' set-up man.
Hideki Matsui also remains on the Sox's radar. A source close to the situation said that the most likely scenario is he re-signs with the Yankees as their DH. Matsui is on record saying he wants to play part-time in the outfield, and that would be an ideal situation for both him and the White Sox.
Free-agent Sox outfielder Scott Podsednik has had conversations on parameters of a deal with the Sox, but according to sources, the team hasn't offered a multi-year deal. Podsednik's agent has talked to the Cubs and Royals as well. Pods wants a multi-year deal but may have to settle for a year and an option with someone.