TODAY, 10:19am: The Braves are not interested in adding Peavy, sources tell David O’Brien of the Atlanta Journal-Constitution (Twitter link).

10:07am: While Peavy remains the pitcher that the club is most interested in dealing, Boston has fielded strong interest in fellow starter John Lackey, tweets Nick Cafardo of the Boston Globe. That is not terribly surprising: since the start of last year, Lackey has logged 306 2/3 innings of 3.64 ERA ball with 7.8 K/9 and 1.8 BB/9. And he is under contract for the league minimum for 2015.

YESTERDAY, 10:12pm: Peavy said that he has spoken with Red Sox GM Ben Cherington and understands that there is a possibility he will be dealt, tweets Pete Abraham of the Boston Globe. “Don’t think people are making stuff up,” he said.

6:31pm: Cardinals GM John Mozeliak says that the team believes it would need to give up one of its own starters to get a “top starter” in return, resulting in a net loss of years of control, tweets Goold.

6:06pm: The Cardinals are “looking for offense not Peavy” right now, reports Derrick Goold of the St. Louis Post-Dispatch (via Twitter). Goold says there is no match with Boston, given that Joe Kelly is expected to return to the rotation in short order.

5:52pm: Boston is discussing starting pitching — not just Peavy — with many teams, but there is “nothing imminent,” a team source tells Abraham (Twitter link).

4:20pm: The Braves are also involved in talks regarding Peavy, reports Pete Abraham of the Boston Globe.

4:16pm: The Cards and Red Sox are in active trade talks regarding Peavy, tweets Jon Morosi of FOX Sports.

12:45pm: ESPN’s Jayson Stark is now also hearing that the Cardinals are interested in Peavy, and he hears that something could come together quickly (Twitter link). The only Red Sox game that the Cards have scouted was the Peavy start that Edes originally referenced, according to Stark.

12:01pm: The Cardinals have had their share of pitching injuries of late, with Jaime Garcia out for the season and Michael Wacha out indefinitely, and Gordon Edes of ESPNBoston.com tweeted yesterday that the team scouted Jake Peavy’s most recent start for the Red Sox. Peter Gammons also tweets that he’s hearing the Redbirds have interest in Peavy.

The 33-year-old Peavy has struggled, to an extent, this season in what has been one of the least-effective campaigns of his 13-year career. He’s posted a 4.64 ERA with 6.8 K/9, 3.4 BB/9 and a 39.2 percent ground-ball rate. His 89.9 mph average fastball velocity is the lowest mark he’s posted since his rookie campaign in 2002. He’s been healthy, however, and has averaged more than six innings per start this season. A move to the NL, of course, could help his numbers as well.

Then again, Peavy wouldn’t need to do much to be an upgrade to the back of the St. Louis rotation. With their current injuries, the Cardinals are using a rotation of ace Adam Wainwright and right-handers Lance Lynn, Shelby Miller and Carlos Martinez (with Joe Kelly set to come off the DL in the next few days). Miller has seen his control disappear, along with his ability to miss bats, and he’s posted a 5.50 ERA over his past nine starts as a result. Martinez has pitched well since transitioning from the bullpen, but he threw just 108 innings last year and is already at 53 in 2014. Marco Gonzales, the club’s 2013 first-rounder, served up 11 runs with more walks than strikeouts in a three-start cameo recently. Peavy could serve as a durable back-end piece to complement veterans Wainwright, Lynn and Kelly while serving as an insurance policy for the club’s younger arms.

Peavy is earning $14.5MM this season and has a vesting player option that he won’t trigger. That option, valued at $15MM, required that Peavy pitch 400 innings from 2013-14, but he is still 144 2/3 frames shy of that mark after spending time on the DL last season. As such, he’s owed roughly $6.58MM over the remainder of the 2014 campaign and will be a free agent at year’s end.

As Edes points out, this isn’t the first time that the Cardinals have had interest in Peavy. The team expressed interest in the former NL Cy Young winner last summer. The Boston Globe’s Nick Cafardo reported over the weekend that Peavy could be of interest to some NL clubs if Boston were to eat some of the remaining salary on his deal.

Jeff Todd contributed to this post.