With Carey Price and backup Peter Budaj between the pipes, and a solid defensive corps, the Habs have lacked a true offensive star up front for years.
Even with Alex Galchenyuk, Lars Eller and Brendan Gallagher performing well as the club's top line, and Max Pacioretty coming on of late, tallying five goals in his last two games, the Canadiens rank 16th in the NHL in goals-per-game, averaging 2.62.
The Habs have roughly $1.74 million in salary cap space and can add a player making just over $3 million, per CapGeek.com, but Bergevin has been quietly dangling some players in an attempt to free up more space, one league source said.
According to the Ottawa Sun, the Canadiens have been trying to move winger Rene Bourque and his $3.3 million cap hit.
Bourque, who has a limited no-trade clause, has two-years left on his contract beyond this season.
The Sun claims the Chicago Blackhawks inquired about Bourque before acquiring Kris Versteeg from the Florida Panthers.
It's unclear who Bergevin has been targeting, as he is not an individual overly willing to talk about potential moves. The Habs have been constantly linked to Winnipeg Jets left wing Evander Kane, and while there were some discussions in the past, it's unknown if those talks were revisited lately.
The Habs have also been engaged in contract discussions with defensemen P.K. Subban, Andrei Markov and Raphael Diaz.
Subban and Diaz can become restricted free agents next summer, while Markov is slated to become an unrestricted free agent.
Bergevin wants all three signed to new contracts, with Subban's being the most costly -- likely seven or eight years, worth at least $7.5 million per season -- though it would not come as a surprise if Diaz is moved in the team's attempt to upgrade it's offensive game up front.