Marc Bergevin, the club's general manager, confirmed as much Monday at the team's annual golf tournament.
"We had interest, we made an offer, and it's a two-way street," the GM said. "If you're interested, the player has to be interested, so I can't comment on why he didn't (accept it), but yes, we did (make an offer)."
Bergevin didn't provide any more details about the offer, reiterating that he didn't want to speculate about why Gardiner wouldn't want to sign with Montreal.
The former Toronto Maple Leafs defenseman inked a four-year, $16.2-million contract with the Carolina Hurricanes on Friday. He became an unrestricted free agent after spending his first eight NHL seasons with the Leafs.
Bergevin also said Monday that the Canadiens have begun negotiating an extension with forward Max Domi.
Gardiner collected 30 points in 62 games with Toronto last season after racking up a career-high 52 points across 82 contests in 2017-18.