With roughly $16 million in available salary cap space, the Habs still need to sign restricted free agents P.K. Subban and Lars Eller.
Subban and Eller are expected to eat up around $11 million in cap space, leaving the team with about $5 million to play with.
Habs GM Marc Bergevin indicated his "phone's never off," and the team could still go after a free agent or complete a trade in order to bolster his lineup.
The Canadiens are believed to still be interested in UFA winger Radim Vrbata, who has four-to-five other teams hot on his trail.
Meanwhile, unrestricted free agent defenseman Francis Bouillon believes he can sign a new deal with the Habs.
"The door isn't closed. I'm confident I can sign a new deal with the Canadiens," he told La Presse, adding that his priority is to re-sign with Montreal.