Jimenez (hamstring) will begin a rehab assignment with the rookie-level Arizona Complex League White Sox on Thursday, LaMond Pope of the Chicago Tribune reports.
Jimenez has been on the shelf for just over three weeks with a left hamstring strain and is now ready to test himself in a game setting. The White Sox haven't revealed how many rehab games the designated hitter might require, but a return from the 10-day injured list next week would seem to be on the table.