The White Sox have elected to keep Peavy fresh in the event he is traded, making him available immediately for any team that might acquire the former Cy Young Award winner. The Arizona Diamondbacks have emerged as the frontrunner to acquire Peavy, a major league source told ESPN.com.
The White Sox announced that Peavy would pitch Wednesday, assuming he is not moved by the 3 p.m. CT non-waiver trade deadline.
Top pitching prospect Andre Rienzo, who arrived in Cleveland on Monday night, will start in Peavy's place Tuesday. The 25-year-old right-hander pitched a seven-inning no-hitter in his last outing Thursday for Triple-A Charlotte. He would become the first player born in Brazil to pitch in a major league game.
Peavy also has been linked in trade rumors to teams like the Boston Red Sox, St. Louis Cardinals, Atlanta Braves, Los Angeles Dodgers and Oakland Athletics. The 32-year-old brought multiple packed suitcases on the road trip in anticipation that he would have to join a new team.
"I'll be happy when Wednesday is here in that there's no more speculation," Peavy said Monday. "I know that there's a good chance I could start (Tuesday for the White Sox) and there's a good chance I won't start.
"I don't know what else to say other than there's a lot of speculation on a lot of people's part. I hear a lot, but at the end of the day I'm listening to my coaches and the front office staff."
On Monday night, White Sox general manager Rick Hahn was asked about Peavy's status and suggested that he is fine with not dealing the veteran, who is signed through 2014 and will make $14.5 million next season.
"With any player who is under contract for future seasons, there certainly is no urgency to make a deal now," Hahn said. "I'm not under any marching orders from (chairman) Jerry (Reinsdorf) or (vice president) Kenny (Williams) to cull payroll at this time. It's more about doing what's the best baseball deal now."
ESPN.com's Gordon Edes contributed to this report.