"I'm not having any discussions on him," general manager Brian Cashman said, according to MLB.com. "His abilities exceed the money that I have."
Cashman told the Web site that his priority is finding a right-handed bat for the outfield.
Damon, a left-handed hitter, batted .282 with a career-high tying 24 home runs and 82 RBIs, but he is 36 years old.
He 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 last weekend. Now, they appear to be backing off.
"He's a valuable player that a lot of teams are talking to, I'm sure," Cashman said, according to MLB.com. "His abilities exceed my physical ability to keep my finances afloat."
The Yankees continuously lead the league in payroll, but there are indications that they aren't willing to go higher than their 2009 levels.
"I'll always try to get the budget pushed, but you're not always successful," Cashman said, according to the Web site. "The Steinbrenner family has been extremely generous for adding talent, but you can't do everything."
Boras has been successful placing many of his clients in Detroit, and the addition of Damon in left field would allow the Tigers to give Carlos Guillen more at-bats at DH.
The Tigers traded leadoff hitter Curtis Granderson to the Yankees in December and lost No. 2 hitter Placido Polanco to the Phillies in free agency, so the top of their batting order is in a state of transition.
Cincinnati's outfield alignment currently consists of Jay Bruce in right field, Drew Stubbs in center field and Chris Dickerson in left. The Reds' leadoff hitters also ranked last in the major leagues with a .650 OPS in 2009.
The catch is, the Reds and Tigers don't appear to have much money left in the budget. Both clubs have been economizing this offseason, and that might be truer than ever now that Cincinnati has signed Cuban pitcher Aroldis Chapman and Detroit has added closer Jose Valverde. Both teams would probably have to get creative to make a run at Damon.
Information from ESPN.com's Jerry Crasnick was used in this report.