The White Sox reinstated Leasure (shoulder) from the 15-day injured list Saturday and optioned him to Triple-A Charlotte.
Leasure (shoulder) made his second rehab appearance for Triple-A Charlotte on Tuesday, striking out one and issuing one walk and giving up no hits over a scoreless inning.
Leasure (shoulder) completed a bullpen session Friday and is scheduled to throw another Tuesday, Scott Merkin of MLB.com reports.
Leasure (shoulder) will begin a throwing program Thursday, James Fegan of SoxMachine.com reports.
Leasure was placed on the 15-day injured list with a right shoulder impingement Saturday, retroactive to July 17, LaMond Pope of the Chicago Tribune reports.
Leasure allowed one earned run on one hit across one inning of work to earn a hold in the first game of Wednesday's doubleheader against the Twins.
The White Sox recalled Leasure from Triple-A Charlotte, James Fegan of SoxMachine.com reports.
The White Sox optioned Leasure to Triple-A Charlotte on Friday.
Leasure allowed one hit and struck out one across a scoreless inning in Sunday's win over the Cardinals.
Leasure earned a save after he pitched two-thirds of an inning, retiring both batters he faced in Sunday's 4-2 win over the Rays.