"I think he'd be a good addition," Braves third baseman Chipper Jones told MLB.com. "He's a guy with experience and he provides us depth at the outfield position."
Atlanta's offer is believed to be for one year and includes deferred money. Damon's agent, Scott Boras, has said he is seeking at least a two-year deal.
Nate McLouth is set as Atlanta's starter in center field, and is the probable leadoff hitter if the team does not add Damon or another outfielder. Matt Diaz is expected to get most of the playing time at one corner outfield spot.
Braves manager Bobby Cox said last week he envisions Cabrera playing all three outfield spots and possibly sharing a position with Diaz.
Cox said the team is prepared to give 20-year-old outfield prospect Jason Heyward a chance to win a starting job in right field. Heyward made only a brief appearance at Triple-A last season and has fewer than 200 at-bats above Class A.
"Well, there's no reason not to give him a crack at making it," Cox said. "If he is too young, that's fine, too. He can spend some time in Triple-A. But if we think he's ready and he can help us, then let's go."
Heyward (6-foot-4, 225 pounds) has the power potential the Braves need in their outfield. He was voted baseball's top prospect by Baseball America after hitting .323 with 17 homers and 63 RBIs at three minor league stops in 2009.
"If he makes the team, he's playing -- lefties, righties, everybody," Cox said.
The Braves' willingness to give Heyward an opportunity could keep them from engaging in a bidding war for Damon. According to reports, Detroit and Tampa Bay also have interest.
Boras did not return a call to The Associated Press on Wednesday. Braves general manager Frank Wren had no comment on Damon.
After four seasons and one championship, Damon won't be returning to the New York Yankees.
Damon, a left-handed hitter, batted .282 with a career-high tying 24 home runs and 82 RBIs last season. But at 36 years old, the Yankees did not want to re-sign him for more than a year.
Damon earned $13 million last season. After back-and-forth in negotiations yielded little, ESPN The Magazine's Buster Olney reported that the Yankees offered Damon a one-year deal in early January but have since backed off.
The Associated Press contributed to this report.