While the Braves have provided an offer, there is still a sense that they will eventually be outbid by the Tigers, who have recently increased their interest in Damon.
But it remains unclear whether the Tigers will be willing to provide the two-year offer that agent Scott Boras is seeking for Damon.
The Rays have also reportedly been a team that could prove to be a fit for Damon.
Coming off a season in which he hit .282 with 24 homers and a .365 on-base percentage, Damon entered the offseason with most teams assuming that he would eventually re-sign with the Yankees.
With Damon having been a prominent player in the Yankees' championship, and having just completed a four-year deal that paid him $13 million a year, he and Boras apparently had expected a vigorous market.
Damon said last month that he told Boras after the World Series that he would "be happy" with a two-year, $22 million contract. But serious talks never seemed to materialize, and the Yankees already had put a $5.75 million offer out to DH/first baseman Nick Johnson when they offered Damon $14 million over two years.
That offer, representing more than a 46-percent pay cut from Damon's previous annual salary, was not accepted. The Yankees signed Johnson, then added outfielder Randy Winn. Damon started receiving interest from other clubs, but there haven't been any reports of any offers approaching the one made by the Yankees.
"We put a value on Johnny, shared that opinion of what that value was, and Scott Boras and Johnny had a different value and a different opinion," Yankees general manager Brian Cashman said last month. "Unfortunately, we never even came close to assessing each other or finding a way to bridge the gap."
Damon, who is currently vacationing in Hawaii, lives in close proximity to where the Braves (Lake Buena Vista, Fla.) and Tigers (Lakeland, Fla.) stage their Spring Training camps.
"I think Johnny's opportunities are many," Boras told ESPN Radio on Wednesday. "There are a number of teams now talking with him. It's that time of year where the clubs get a real good chance to sit around the table and look in the mirror and say, 'Do we have the talent to fulfill our goals and expectancies for the upcoming season?'"
Braves GM Frank Wren has indicated that he is happy with the current makeup of his club. But at the same time, he recognizes the value that Damon could bring the club while serving as the legitimate leadoff hitter that it currently lacks.
"I think he'd be a good addition," Chipper Jones said. "He's a guy with experience, and he provides us depth at the outfield position."
When the Braves have pursued top free agents in the past, they have often asked Jones to serve as a recruiter. The veteran third baseman did not confirm whether the Braves had asked him to contact Damon.