A team leader and dominant pitcher for eight years, Peavy knows San Diego and its fans. He felt the Padres were close to becoming something special in the mid-2000s before it all came apart.
Rebuilding his career in Chicago after a complicated surgery last July repaired a torn latissimus dorsi muscle in his back, Peavy sees how similar the situation in San Diego is to what has been going on with the Dodgers: Ownership instability and limited budgets lead to underachievement on the field, creating unrest and disaffection in the fan base.
When Earvin "Magic" Johnson became the face of the Dodgers' new ownership group earlier this month, everything seemed to change in Chavez Ravine, optimism replacing cynicism.
Johnson and the Guggenheim Baseball Management group made bold vows of commitment to returning the franchise to its glories of old. Because it was Magic, a man as beloved and trusted as any athlete in the city's history, Los Angeles believed.
This is where Gwynn steps into the picture in San Diego. What Magic is to L.A., Gwynn is, with a lower national profile, to the border town down Interstate 5.
"Tony is the most respected, respectable figure in San Diego," Peavy said before the White Sox took on the Angels. "I mean, everybody loves the guy down there.
"I can't see how it could be anything but a good thing for Tony to be involved in ownership. It would mean a lot to the fan base, I promise you."
Gwynn, who shared the unofficial Mr. San Diego designation with the late Junior Seau, reportedly has ties with a group interested in buying the Padres from John Moores.
A Hall of Famer who spent his entire 20-year career with the Padres, Gwynn is the coach of San Diego State's baseball team and father of Dodgers outfielder Tony Gwynn Jr. Among the players who have come through Gwynn's program in his 10 seasons is Nationals ace Stephen Strasburg.
An eight-time NL batting champion, Gwynn is immortalized not only in Cooperstown, N.Y., but also at Petco Park. His perfect left-handed swing is captured in a 10-foot bronze statue beyond the outfield fence. His No. 19 is among six retired by the organization.
For all of his remarkable achievements -- 3,141 hits, .338 career average, 15 All-Star Game appearances, five Rawlings Gold Gloves -- Gwynn is embraced for his demeanor and personal style. He's never big-timed anyone, remaining accessible and visible throughout the San Diego area.
Even though he reached San Diego State, starring in basketball as well as baseball, as a teen and never left his adopted city, Gwynn's early years were spent in Long Beach, up the coast, near Los Angeles. This is a mere footnote, however.
Tony Gwynn is as San Diego as perfect weather and gorgeous beaches.
While it certainly wouldn't compare in magnitude nationally to Johnson assuming an active role in Dodgers ownership, Gwynn would have a similar impact with the public perception of the Padres.
"I was around Tony enough to know how knowledgeable he is about the game," Peavy said. "I don't know how much of an impact he'd have [in performances] on the field, but he'd definitely bring a lot of positive energy and buzz around town with the fans. That can trickle down from the stands to the field.
"When the fans are excited, you feel it and react to it as a player. That can't hurt. Look at what the Dodgers have done since Magic and his people got there."
Not a bad formula for San Diego to follow.
Gwynn, according to media reports, met on Tuesday morning with Thomas Tull, a prospective buyer of the Padres, at a downtown San Diego hotel.
Tull is the founder of Legendary Entertainment and Legendary Pictures, based in Burbank, Calif. In 2005, the company reached an agreement to co-produce and co-finance 40 pictures with Warner Brothers.
Among the 23 films co-produced by Legendary Pictures are such hits as "The Dark Knight," "The Hangover," "Clash of the Titans," "Inception" and "The Hangover II."
Tull is a member of the San Diego Zoological Society's board of directors.
Gwynn, had cancer surgery in August 2010. A second procedure, on Feb. 15, removed a malignant growth from the inside of his cheek.
The Hall of Famer was back on the bench for the first time this season on Tuesday in his Aztecs' victory over Loyola Marymount.