The White Sox on Sunday scratched Peavy from his scheduled start Monday against the Kansas City Royals due to back spasms.
"[Sunday] I really threw for the first time without it grabbing me pretty hard," Peavy told reporters, according to The Chicago Tribune. "Two days ago it was still grabbing me pretty hard, and I had to be relatively pain-free two days prior to me pitching. That was two days ago. If I was pitching [Monday], I wasn't ready.
"But the way I felt today, with a few more days of treatment, I can't see Wednesday night I won't be on cue."
The newspaper reported that Peavy also took part in fielding drills and throwing to test out his back.
Peavy has not pitched since April 26 after being scratched from a Thursday start when his back stiffened up while warming up. He is 3-1 with a 3.38 ERA in five starts this season.
Information from The Associated Press was used in this report.