Manager Ozzie Guillen confirmed before Saturday's game against the Arizona Diamondbacks that Peavy will be back from a mild strain of his right groin after just one rehab start.
Peavy has been on the disabled list retroactive to June 6. A 15-day stint on the disabled list would make him eligible to return Tuesday. The White Sox play host to the Cubs for a three-game series beginning Monday.
"Jake will start against the Cubs one of those days," Guillen told reporters in Arizona. "I don't like hiding behind things and having mystery. Yeah, he will start there. Hopefully he can be in there and stay healthy and doesn't have to go back to do the same (recovery) he's had to do all year."
In Peavy's rehab start Thursday with Triple-A Charlotte, the right-hander pitched six scoreless innings. He had nine strikeouts and didn't allow a walk.
He made five starts after returning from surgery last summer to reattach his latissimus dorsi. He was 2-1 with a 4.66 ERA over 29 innings.
Doug Padilla covers the White Sox for ESPNChicago.com.