Jimenez (abdomen) was cleared to run the bases Tuesday and could resume swinging by the weekend, James Fegan of The Athletic reports.
The White Sox have yet to set a date for Jimenez's return, but he was given a 4-to-6 week recovery timeline following his appendectomy earlier this month. Gavin Sheets and Adam Haseley have split reps in right field since Jimenez landed on the injured list.