Backstrom, the Wild's winningest goalie in franchise history, is believed to be looking for a three-year contract worth around $4 million per season.
The 35-year-old is wrapping up a four-year, $24 million contract.
Backstrom posted a 24-15-3 record with the Wild this past season, along with a 2.48 goals-against-average and a .909 save percentage.
The Helsinki, Finland, native has played in 369 career NHL games, all with Minnesota. Over his career, Backstrom has a 184-124-45 record with a 2.43 goals-against-average, a .917 save percentage and 28 shutouts.