Reilly has 10 points (two goals, eight assists) in 38 games this season.
"He's a good skater," Montreal general manager Marc Bergevin said. "He's still young, I mean, at 24, he didn't play a lot of NHL experience, so he's still has a chance to play. And if you look at Minnesota with (Jonas) Brodin and (Ryan) Suter on the left side, I thought he became expendable for them. So the term used, he's not a slam dunk, but he has a chance and that's what we hope for him."
Chosen by the Columbus Blue Jackets in the fourth round (No. 98) of the 2011 NHL Draft, Reilly did not sign a contract with them and signed with the Wild as an unrestricted free agent July 1, 2015.
"I don't know how far we can go on the offensive side, but he has potential," Bergevin said. "I saw him play recently and I think he has good sense. Will he continue to develop in a new organization? That's possible. We will surely support him and help him get to that level, and the rest remains to be seen."
The Wild (35-20-7), who host the St. Louis Blues on Tuesday (8 p.m ET; NBCSN, NHL.TV), are in third place in the Central Division, three points ahead of the Dallas Stars.
The Canadiens (23-29-9), who host the Philadelphia Flyers on Monday (7:30 p.m. ET; NBCSN, RDS, TSN2, NBCSP, NHL.TV), are 12 points behind the Columbus Blue Jackets for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.