The right-hander has a history with Arizona general manager Kevin Towers. Peavy pitched for Towers for eight seasons when Towers was the GM of the Padres.
It was Towers who traded Peavy to the White Sox at the Ttrade Deadline in 2009 in exchange for Dexter Carter, Aaron Poreda, Clayton Richard and Adam Russell.
Peavy is owed around $5.28 million for the rest of this season and $14.5 million next year. The contract includes a player option for 2015 if Peavy has either 400 innings pitched in 2013-14, including at least 190 in 2014, and is not on the disabled list at the conclusion of the 2014 season.
Peavy is also owed a $4 million buyout from his previous contract.
What the D-backs would have to give up to get Peavy is not known. The White Sox are interested in acquiring infielders, and the D-backs do have highly regarded prospects like third baseman Matt Davidson and shortstop Chris Owings at Triple-A Reno.
If the White Sox require a young pitcher in return, it's possible the D-backs could include left-hander Tyler Skaggs in the deal.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.