Jake Peavy told Joe Cowley of the Chicago Sun-Times that he would ask for a trade if the White Sox start a complete rebuilding process. That doesn't seem likely, and Peavy tells Cowley he feels good about his situation in Chicago, despite the team's 25-33 record. Before the White Sox became sellers, Peavy told MLB.com that he doesn't have interest in playing for a rebuilding team.
Peavy has a full no-trade clause and proved last summer that he isn't afraid to use it. Two months before the Padres traded Peavy to the White Sox, he vetoed a deal that would have sent him to Chicago. Ironically enough, the 34-24 Padres are now in contention, but they would presumably be looking for bats, not arms if they decide to deal.
Peavy, 29, has $42.6MM remaining on his deal, so few teams could afford him. His 5.90 ERA could turn clubs off, though Peavy's peripheral numbers suggest he has pitched better than his ERA would have you believe. The right-hander's salary and stats would make him hard to trade and the White Sox don't seem likely to start a complete rebuilding process, so it doesn't look like Peavy's going anywhere.