Damon, 35, is in the final season of the four-year, $52 million contract he signed after leaving the Boston Red Sox.
Damon said the numbers game in the Yankees outfield does not bode well for him. Melky Cabrera and Brett Gardner are in center, Nick Swisher and Xavier Nady -- who will also be a free agent and is currently on the DL -- in right and the team's top prospect, Austin Jackson, lighting up Triple-A.
Yankees GM Brian Cashman has spoken about making the Yankees younger.
"I know where I want to be next year," Damon told 1050 ESPN New York. "I want to be here in New York. I also know New York has a lot of young outfielders coming back. Austin Jackson is in the wings. At least, in this situation, I know my chances of coming back could be slim because of the young talent the Yankees do have."
Damon entered Friday night's game with the Angels, hitting .295 with four homers and 10 RBIs. He has picked up those numbers batting second in the Yankees' order.
When the Yankees signed Damon in 2005, they envisioned him as a center fielder and leadoff hitter. Damon -- who at one point as a Yankee considered retirement -- said this situation is different than what he faced in his final year with the Red Sox.
"I just go out and play," Damon said. "What happened before, I think, everybody in the world thought I was going to re-sign with Boston. Everyone thought I was going back. Here, people don't really know. Everyone is pretty much thinking this could be my last year here so I think that is a difference. I went out as a free agent in Boston and had a great year and I priced myself out of there market, at the time. Hopefully, I can go out and have a good year and they can see how important I am with the other players with doing the recruiting and doing whatever this team needs me to do. I've enjoyed playing here."
He is savoring this season and hoping he can change the Yankees' mind, though, he doesn't sound totally optimistic.
"If I go out and play the game well and play the game right, there obviously will be some interest," Damon said. "But I understand the business of this. I've been a free agent twice already."
Andrew Marchand is the managing editor of 1050 ESPN Radio in New York.