Bourque, according to one source, is aware of a possible move and appears welcoming of a change.
The Habs are also looking for a top-six power forward, something they've been trying to add for the last two seasons.
It's unclear if trade talks with the Winnipeg Jets over left wing Evander Kane are still ongoing, but he has been someone the Canadiens have been interested in since last summer's NHL Draft.
The Canadiens are also trying to get star defenseman Andrei Markov locked up to a new contract.
Markov, 35, is scheduled to become an unrestricted free agent and is looking for a three-year contract.