"I don't see us in the situation as say some teams that are talked about around the league," Peavy told MLB.com. "This team here can really, really pitch. We have good offensive players, too.
"We have what it takes. You watched this same team play good baseball last year. You look at a team like Boston, talked about toward the end of last year as one of the worst teams in the league, and they are almost 20 games over .500 playing as good of baseball as you can play now.
"I don't see this team as going on some long, long rebuilding where you can chalk up the next three or four years," Peavy said. "I can't see that happening. I certainly hope that's not the case."
Peavy reported general soreness after his 53-pitch bullpen session Friday, but the good kind of soreness coming from the raising of his workload. He will throw a simulated game Tuesday in Detroit as the next recovery step from a fractured rib on his left side, and Peavy understands that recovery could lead to a deal before the July 31 non-waiver Trade Deadline.
It's not what Peavy wanted when he returned to the White Sox with a two-year, $29 million deal this past offseason before free agency began. But he also is fully aware that when a team projected to contend ultimately underachieves, moves will come regardless of the future prospects.
A healthy Peavy could warrant a young impact talent in return.
"Obviously leaving Chicago would be such a bummer for me in a ton of ways. I don't want to leave the relationships and the city," Peavy said. "I came back here because I felt like there was a little bit of unfinished business for the team in general.
"There's nothing more that I want than to be a part of a winner here in Chicago with this group of guys. We'll see how it plays out. I'm open to anything and I'll do everything I'm asked to do. If that's staying here, I'll be happy to do that. If that means to move, then that's something we'll address and be OK with when that time comes."
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.