On the flip side, the Habs were concerned about his disappointing performance in the first half of the season.
Briere, a native of Gatineau, Quebec, recently spoke with Canadiens GM Marc Bergevin and head coach Michel Therrien, which resulted in the team shopping the 36-year-old.
It was widely reported that the Canadiens and Buffalo Sabres had been discussing a deal involving Briere, but talks have quieted and the Sabres are on the verge of hiring Ottawa Senators assistant GM Tim Murray as their new commander in chief.
Murray, once officially hired by Buffalo, and Bergevin could continue trade talks, but a recent injury to Canadiens youngster Alex Galchenyuk might keep Briere in Montreal for the next six weeks.
Galchenyuk broke his hand on Monday night and will need up to six weeks to recover.
The Canadiens have been searching for a top-six forward with an eye for the net for most of the season, having inquired about such players as Winnipeg Jets left wing Evander Kane, and losing Galchenyuk could keep Briere around if Bergevin's unable to make a move for a sniper.
Briere scored two goals and added one assist on Saturday, playing with Tomas Plekanec and Brian Gionta, after being scratched from the line up and after rumors swirled over a possible trade.
In 31 games with the Habs so far this season, Briere has registered seven goals and six assists for 13 points.