The 27-year-old All-Star would be a great fit for the Wings, who have a gaping hole in their defense now that Nicklas Lidstrom has retired.
However, Preds GM David Poile has reportedly presented a "firm" offer to Suter and is expected to tender a similar offer to defensive partner Shea Weber, which could sway Suter to stick in Nashville.
Suter collected seven goals and 39 assists for 46 points for the Predators in his seventh NHL season. He finished tied for sixth among defensemen in assists, which is where his value will come into play for the Red Wings and the several other teams looking for a boost on the back end.