The White Sox return to Detroit for a four-game series from July 11-14 and again for a three-game set from Aug. 30-Sept. 1.
Luis Pujols was named interim manager earlier Monday after the Tigers fired Phil Garner and general manager Randy Smith.
Detroit is off to an 0-6 start, its worst in a decade.
"The rainout day helps. Maybe we'll get some (injured) people back," Pujols said. "I'm going to take a day or two and see what happens. Nothing's going to happen in the next couple of days. We're just going to try to get everyone healthy."
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