By Thursday evening Peavy had nixed the trade, the Chicago Sun Times and Chicago Tribune reported.
Agent Barry Axelrod told ESPN.com's Jerry Crasnick that Peavy had a "strong preference" to stay in the National League. That preference, along with Peavy's fondness for his new home in Southern California, apparently spelled the end of the deal.
"We aren't hiding anything from anybody. Jake has a strong preference to stay in the National League. He has a comfort zone there, he's been successful, and he's won a Cy Young Award. I don't know that on May 21, that preference has eroded very much. From our point of view we may say, 'Let's give [the Padres] more time and see if a National League team might step up over the next six weeks.'
"If this were any one of three or four other teams and they called about him, Jake would jump at it. He would be willing. They know who they are. They know that certain places are more enticing to him."
Axelrod said that Padres general manager Kevin Towers spoke to him Wednesday and indicated that a trade with the White Sox was on the "front burner." But Axelrod and Peavy had less than a half-hour to discuss the potential move to Chicago, and they planned to speak again Thursday.
Peavy called White Sox right-hander Scott Linebrink last night for his opinion about going to Chicago and got strong feedback, ESPN's Peter Gammons reported.
"Jake called me [Wednesday] afternoon to ask about what it's like here in Chicago," said Linebrink, according to ESPNChicago.com's Levine. "I think he's ready to move on, but I can't tell you for sure he's going to accept the deal. Losing 100 games, like they did last year, wears on a player."
Linebrink was Peavy's teammate in San Diego.
Peavy's preference for the National League and his fondness for California would appear to put the Los Angeles Dodgers high on his wish list. But any deal between San Diego and L.A. would be complicated by the fact that the teams are divisional rivals and are located about two hours from each other.
Even if the Dodgers were interested in putting together a package for Peavy, which is uncertain, they do not have much of a trading history with the Padres.
The Chicago Cubs were also mentioned as a possible suitor for Peavy throughout the offseason.
Peavy's contract includes a full no-trade clause for both this year and 2010. It shifts to a partial no-trade clause in the final two years of his deal in 2011 and 2012.
Axelrod said if Peavy consents to a trade, he will insist upon having a no-trade clause for the duration of the contract. If Peavy were to remain in San Diego, he would attain his 10-and-5 service time (10 years in the majors, five years with the same franchise) and have the right to veto any deal starting in 2012.
According to Axelrod, Peavy might also be more inclined to ask for financial concessions -- such as a contract extension -- if he agrees to go to a team that isn't high on his list of preferred sites.
"If it's a team that Jake deems to be very desirable, he might be looking for something on the minimal side," Axelrod said. "If it's a team where he feels he's sacrificing some things -- geographically or otherwise -- he might ask for more."
Peavy, who won the 2007 NL Cy Young Award, has an 89-67 career record with a 3.27 ERA. In 2007 he earned the pitching Triple Crown by leading the National League with 19 wins, 240 strikeouts and a 2.54 ERA.
Peavy is due to earn $11 million this season. Towers has said the Padres are about $5 million above the $40 million player payroll that the team's majority owner, John Moores, has set for this season, according to the Union-Tribune.
Peavy is currently 3-5 with a 3.82 ERA for the Padres, who are 18-22 and third in the NL West, 10 games behind the first-place Los Angeles Dodgers.
ESPN.com's Jerry Crasnick, ESPN baseball analyst Peter Gammons, ESPN The Magazine senior baseball writer Buster Olney and Bruce Levine of ESPNChicago.com contributed to this report.