Selected No. 2 in the 2003 NHL Draft by the Hurricanes, Staal has scored 1,031 points (439 goals, 532 assists) in 1,272 regular season games for the Sabres, Wild, New York Rangers and Hurricanes, and 51 points (21 goals, 30 assists) in 62 playoff games.
He scored 10 points (three goals, seven assists) in 32 games for the Sabres this season.
Staal said he's spoken with Canadiens general manager Marc Bergevin and coach Dominique Ducharme.
"I've told them both I just want to win," Staal said. "I want to be out there and win and be competitive and try to help our group win games, wherever that is in the lineup. I will do what I can."
Staal's role might be limited with the Canadiens, who also have Phillip Danault, Nick Suzuki and Jesperi Kotkaniemi at center.
"I'm always striving to have my name called as much as I can because I'm competitive, I want to play, I want to do what I can to help…," Staal said. "but I also understand, 'Hey, this night or this moment might not be mine, it might be someone else's.' You need to be supportive and be a good teammate and that's what I'll do and what I have done over my career."
Staal said he's excited by the pace and transition game of the Canadiens and impressed with their defensemen anchored by Shea Weber and Jeff Petry, and goalie Carey Price.
"There's a balance up front that can come at you in waves," he said. "With the amount of games we have, the type of season it is, you're going to need everybody in your lineup. … I just think there's a lot of mix of some guys that have been around a while and understand the game."