Right-hander Jacob Turner was recalled July 17 from Charlotte and has made two starts in Rodon's place, losing both games and not lasting past the fourth inning in either.
It's unknown when Rodon will be activated or when Sale will pitch next. Sale will be eligible to pitch Thursday, when the White Sox play the second of two games against the Cubs at Wrigley Field, but the decision hasn't been made.
"We will list it as 'TBA' right now, but we will likely announce something in the coming days as to how we will handle the rotation," Hahn said.
Miguel Gonzalez is scheduled to start against the Cubs on Monday, followed by James Shields on Tuesday, before the rivalry series shifts from U.S. Cellular Field to Wrigley Field for the final two games. Turner is slated to start Wednesday.
The White Sox recalled right-hander Anthony Ranaudo from Charlotte on Sunday to give the pitching staff a fresh arm for the finale of the series against the Tigers and the remainder of Sale's suspension. Reliever Matt Albers started in Sale's place for Saturday's game, which was suspended by rain after eight innings, and he was followed by five more relievers.
"It's a tough day, knowing we have to finish the game that was last night and then continue on with this one," White Sox manager Robin Ventura said. "You're light in the bullpen to be able to do that."
• Ventura said injured second baseman Brett Lawrie, who's day to day with tightness in his left hamstring, is progressing well. Lawrie left the series opener against the Tigers after three innings because of the injury and sat out the next two games. Lawrie was available off the bench on Sunday.
• Infielder Carlos Sanchez was recalled from Charlotte to be the White Sox 26th man for the second game of Sunday's quasi-doubleheader.
Brian Hedger is a contributor to MLB.com based in Chicago. This story was not subject to the approval of Major League Baseball or its clubs.