"I would love to come back here to New York, but I also know other teams are calling to have me go and help them win a championship," Damon said, according to the New York Post.
"I've loved my time here. Hopefully, it's not over, but we just have to wait and see what New York comes to offer. We're listening to anybody out there."
Yankees general manager Brian Cashman has said that he plans to reach out to the club's own free agents first, which includes not only Damon but Hideki Matsui and Andy Pettitte. The Yankees are holding organizational meetings in Tampa, Fla. next week, at which time Cashman will be provided his budget for 2010.
Damon, 36, hit .282 with 24 home runs and 82 RBIs in 143 games for the World Series champions in 2009, his fourth year in a Yankees uniform after playing the previous four seasons with the Red Sox.
The 15-year big league veteran has also played with the Royals and Athletics. Though his time in New York has been marked by various aches and pains, they held off long enough for him to have a productive year, including contributing one of the great baserunning moments in World Series history against the Phillies.
"I feel like I can play another 10 years," Damon said. "It's just a matter if I want to. My body has held up great for me over the years. I feel great now. I felt great during the season.
"I know what's here in New York -- you have the new stadium, you have the great coaches, you have the great players. You guys tell Cash to get things going with me. I'm up for it."
Damon is planning to leave the country on a European vacation with his wife, Michelle. Making a reference to the character in the 1996 movie 'Jerry Maguire' who yelled, "Show me the money!," Damon said that he has no plans to make a cameo appearance at the Winter Meetings, which kick off Dec. 7.
"I really don't think I need to go to Indianapolis and do the Rod Tidwell walk down free-agency row," Damon said. "I think teams know what I can bring."