Fletcher could find a short-term fix in Toronto Maple Leafs goalie James Reimer, who has one-year left on his contract beyond this season.
The Maple Leafs are willing to move Reimer, as well as several other players, as they look to retool for next season.
Sitting eight points out of a playoff spot in the West, Minnesota plans on making a push for post-season play, but want an upgrade in goal.
Reimer helped the Maple Leafs into the playoffs in 2012-13, but has since lost his starters job to Jonathan Bernier.
The Wild has also been linked to Carolina Hurricanes goalie Cam Ward, who has a no-trade clause and would have to approve any deal the team tries to make.