His priority has been to re-sign with the Coyotes, if the team remains in Phoenix, and all signs now point to that happening.
The Wings wouldn't provide an update on the situation, telling MLive.com that they remain in the hunt.
"I've been in communication with the Doan camp a number of times throughout July," said Red Wings GM Ken Holland. "We have interest."
The Pittsburgh Penguins, Vancouver Canucks, New York Rangers, Philadelphia Flyers, Montreal Canadiens and Nashville Predators are also keeping an eye on Doan's availability.