CLEVELAND -- Chicago White Sox pitcher Jake Peavy, who has been involved in multiple trade rumors in advance of Wednesday's non-waiver trade deadline, will not make his scheduled start Tuesday.

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.