Damon made $13 million in the final season of a four-year, $52 million deal he signed after leaving the Boston Red Sox in free agency.
New York's acquisition of center fielder Curtis Granderson from Detroit, as part of a seven-player, three-team swap that included Arizona, was finalized Wednesday.
"I don't think it affects what I can still do. Either they come out and pursue me or they don't," Damon told the New York Post. "I still know how to play baseball and will make any team better."
Damon was New York's primary left fielder in 2009 and averaged 144 games in the last four years. He hit .282 with a career-high-tying 24 home runs, 82 RBIs and 107 runs scored as the Yankees won their first World Series since 2000.
Information from The Associated Press was used in this report.