"I would say that we are making progress," said Peavy's agent, Barry Axelrod, from the Winter Meetings in Nashville. "It's pretty encouraging."
A report on FoxSports.com on Sunday said the Padres and Axelrod were close to a three-year extension with an option for a fourth year. Peavy's current deal expires after 2009.
A high-ranking Padres official expressed his optimism Sunday that the deal will get done.
Axelrod said that he doesn't expect any imminent announcement regarding Peavy's deal, as the Padres will push ahead this week with plans to improve their offense, particularly finding an offensive-minded outfielder, like Japanese free agent Kosuke Fukadome.
San Diego general manager Kevin Towers and Peavy weren't available for comment late Sunday, as Peavy was returning to his home in Alabama from a hunting trip.
That the Padres and Peavy's camp were talking isn't exactly news, as the two sides have had discussions since Peavy won the Cy Young Award last month.
On Friday, Towers told reporters that his contact with Axelrod about Peavy was "almost daily," and that "as of now, we're moving toward an extension."
Peavy's contract would be the largest in franchise history, surpassing the four-year, $34 million contract Phil Nevin signed in 2001.
Peavy, the unanimous winner of the Cy Young Award after leading the National League in victories (19), strikeouts (240) and ERA (2.54), is currently under contract through the 2009 season.
Peavy will earn $6.5 million next season, with the Padres holding an $11 million option on him for 2009.
Now it appears that Peavy -- the team's 15th-round pick in the 1999 First-Year Player Draft -- will be in San Diego long after his current deal expires.
"I know what I can get on the open market, but if I get to the open market, it won't be about the money," Peavy said last month. "This team has given me financial security for this Alabama boy's life. I'm very comfortable to be where I'm at."
Elsewhere, the Padres still haven't formally announced the signing of free-agent pitcher Randy Wolf, though the left-hander is said to have agreed to a one-year deal worth $4 million, though the deal could grow to $9 million with incentives.
That could mark the end of San Diego's flirtation with another free-agent pitcher, Matt Clement. Clement would like to pitch in San Diego, though he has other offers, said Axelrod, his agent.
Axelrod didn't think the Padres were willing to take on more than one pitcher coming off an injury.