Paul Konerko will begin a rehab assignment at Double-A Birmingham on Thursday.
A lower back strain forced the veteran first basemen to the disabled list at the beginning of the month.
If all goes well for Konerko he could be activated on July 22. On the season Konerko was hitting .249/.314/.368 with 7 home runs and 30 RBI in 67 games.
The White Sox have already traded reliever Matt Thornton and have previously indicated that everyone but Konerko is available via trade.