The Habs have been linked to Winnipeg Jets left wing Evander Kane since last summer's NHL Draft, and while inquiries were made earlier in the season, it's uncertain if the two teams are still in discussions.
Bergevin has several pieces he is willing to move off his roster, including veterans Brian Gionta and Rene Bourque, though their high salaries are likely to keep a deal from happening.
Meanwhile, the Canadiens remain in talks with Andrei Markov's agent, former NHL forward Sergei Berezin, over an extension.
Montreal initially pitched Markov a one-year extension, but is believed to be willing to go to two-years on a contract.
Markov, 35, wants to play out the rest of his NHL career with the Habs, but also wants a three- or four-year deal.
The Habs have received one significant trade offer for Markov, a source with knowledge of the situation told TFP, though the team remains hopeful they can come to terms on an extension.
Negotiations between the two sides will continue between now and the March 5 trade deadline.