Leasure (shoulder) completed a bullpen session Friday and is scheduled to throw another Tuesday, Scott Merkin of MLB.com reports.
Leasure has been on the shelf since July 20 with a right shoulder impingement, but has completed a pair of bullpen sessions and has a third on tap. It's unclear if the White Sox plan on sending Leasure on a rehab assignment, but the 25-year-old should be expected back in the first half of September.