Tootoo, 30, started his NHL career with the Predators after being drafted by the club in the fourth-round (98th overall) of the 2001 NHL Entry Draft.
The Wings signed the native of Churchill, Manitoba, as an unrestricted free agent to a three-year, $5.7 million contract on July 1, 2012.
Wings GM Ken Holland has been looking to shed some salary, so he can add a defenseman and re-sign free agent veteran Daniel Cleary, but he's not been able to find a partner.
FoxSportsDetroit.com also claims the Wings are shopping forwards Mikael Samuelsson, Todd Bertuzzi and Cory Emmerton.
In 42 games with Detroit last season, Tootoo registered three goals, five assists and 78 penalty minutes.