Thorpe (forearm) threw from 60 feet on Aug. 15, MLB.com reports.
Thorpe (forearm) will begin a throwing program Thursday, James Fegan of SoxMachine.com reports.
The White Sox placed Thorpe on the 15-day injured list Friday with a right flexor strain, James Fegan of SoxMachine.com reports.
Thorpe (3-2) took the loss Friday, surrendering eight runs on six hits -- including three home runs -- and two walks in only 0.2 innings as the White Sox were routed 10-0 by the Mariners. He struck out one.
Thorpe didn't factor into the decision in Sunday's 4-1 loss to the Royals. He pitched six scoreless innings, allowing three hits and two walks while striking out five.
Thorpe didn't factor into the decision Wednesday against Minnesota in the second game of a doubleheader, allowing two runs on three hits and a walk through six innings. He struck out one.
Thorpe (3-1) picked up the win Friday, allowing one run on three hits and two walks over 6.1 innings in a 3-2 victory over the Marlins. He struck out five.
Thorpe (0-1) took the loss Sunday against Arizona, allowing eight runs (seven earned) on six hits and five walks with no strikeouts over 3.1 innings.
Thorpe is scheduled to start Sunday's game against the Diamondbacks at Chase Field.
The White Sox selected Thorpe's contract from Double-A Birmingham, and he'll start Tuesday's game against the Mariners.