While the Wings have approximately $13 million in available cap space, the asking price for the veteran winger is reportedly too high for the team.
The Red Wings have been looking to boost their offense up front after being eliminated in the first round of the Stanley Cup Playoffs this spring, while trying to bolster their blueline since the retirement of captain Nicklas Lidstrom and departure of Brad Stuart.
Meanwhile, USA Today has reported that the Nashville Predators are among the 16 teams attempting to sign Doan, who has met with different clubs this past week.
"He is an outstanding player and outstanding person," Predators head coach Barry Trotz said of Doan. "He really would be a type of player we would want on our hockey club and we are exploring that like a lot of other teams."
Doan has reportedly given prospective buyer Greg Jamison a deadline of Friday to show progress in keeping the team in Phoenix.
"If he is available, I know we will be high on his list because I know one of the things he's looking for is a team with a chance to win," Trotz said. "I'd check that off because he believes we are."