Backstrom, 35, posted a 24-15-3 record with the Wild this season, along with a 2.48 goals-against-average and a .909 save percentage.
The Helsinki, Finland, native is wrapping up a four-year, $24 million contract.
Wild GM Chuck Fletcher would like to keep Backstrom, but failing that, he could pursue the trade market for help between the pipes.
The Los Angeles Kings are looking to trade goalie Jonathan Bernier, the St. Louis Blues are willing to move one of Jaroslav Halak or Brian Elliott, the Anaheim Ducks are dangling Jonas Hiller, the Buffalo Sabres are trying to deal Ryan Miller, and if the Toronto Maple Leafs get their hands on Roberto Luongo, James Reimer could become available.
Meanwhile, Star-Tribune also reports the Wild has initiated contract talks with restricted free agents Cal Clutterbuck and Jared Spurgeon.