Instead, Peavy took a Wes Timmons line drive squarely off his right elbow during Minor League rehab start No. 3 on Monday night, and more will be known about how he responds after a scheduled side bullpen session prior to Wednesday's contest.
"Obviously, getting hit last night [by a liner] was not what we expected, not what we wanted, especially after the first few innings were encouraging," Peavy said Tuesday. "The effort last night was encouraging. I felt quite a bit better than I had the previous two and it was something to build off of.
"This is a tiny setback, but we'll just have to wait and see how we feel. I didn't play any catch today, but hopefully tomorrow or the next day, we'll go back on the mound, flush some of the soreness out and get back out there really soon.''
Separating Monday's encouraging effort from the mishap with the line drive was almost impossible for Peavy. But there was no question that Peavy took another major step forward by hurling five scoreless innings against Gwinnett for Triple-A Charlotte.
If he didn't take the line drive, flush enough for it to leave seam marks on his pitching elbow, Peavy certainly would seem set up to face the Yankees.
"I certainly felt good last night, going out for the fifth," Peavy said. "If I wouldn't have got hit, I would have pitched more. I was going to throw more pitches. The final count was 80, and I was looking to stretch it out to even 100 or so, and I felt like I could have done that.
"You take a ball off your pitching elbow and it hits you flush, you're going to have to come out of the game. It would be to hard to separate, but I certainly feel like I was getting close last night, before the incident happened.''
White Sox manager Ozzie Guillen and pitching coach Don Cooper didn't alter their stances on the matter from Monday night. If Peavy is healthy and feels ready to compete at his desired level, they will welcome him into the rotation.
Otherwise, the White Sox believe they have other options at Charlotte in Dan Hudson and Carlos Torres. Cooper ruled out middle reliever D.J. Carrasco from stepping up and making the start because he's too valuable in his current role.
Cooper remained hopeful that Peavy's elbow will respond well enough to get him out to the mound.
"My comment to him was, 'Hopefully you getting hit in the elbow won't get in the way of your next start,'" Cooper said. "Where that is? I don't want him to miss his next start, but we'll see how it goes. If he has to take it another day, we'll see.
"That will unfold the next day and see how he feels. He was much more positive about his outing, he was climbing. Everything he's saying is more positive and heading in a good direction. But he's still going to be the one making the call, more than anyone else."
Guillen said the only certainty was that Jose Contreras was staying put in the bullpen.
"Jose is not starting for sure," Guillen said. "I got three kids and I want to see my grandkids when they are born. I don't want to get a heart attack before my time.
"We did everything we could to protect Jose to give him the most opportunities we could. But we can't deal with this anymore. Unfortunately, we were waiting for him to turn around and do it and he couldn't do it."