If Fletcher is unable to trade Gilbert and his $4 million cap hit, the team is expected to buy him out.
The buyout period is currently open, though players must first clear waivers, and expires at 5pm ET on July 4.
Gilbert, 30, is scheduled to earn $3 million next season.
In 43 games with the Wild this past season, Gilbert registered three goals and 10 assists for 13 points.
The Wild is also entertaining offers for forward Cal Clutterbuck, who is set to become a restricted free agent, however the team is also negotiating an extension with him.