Perry can become an unrestricted free agent July 28.
"There's still a lot of good hockey left in me and I would love to come back here and experience Montreal for being Montreal," the 36-year-old said Friday. "It was a weird year, the family not being here and all that, but yeah."
Perry signed a one-year, $750,000 contract with Montreal on Dec. 28 and scored 21 points (nine goals, 12 assists) in 49 regular-season games, with 10 points (four goals, six assists) in 22 Stanley Cup Playoff games. He played in the Stanley Cup Final for the second consecutive season after getting there with the Dallas Stars in 2020, losing to the Tampa Bay Lightning each time.
He said he's had discussions with Canadiens general manager Marc Bergevin, "but not to the extent where we're hammering something out."
"I did tell him I'd love to come back and be a part of this and see what we can do again next year," Perry said. "You get so close and you taste that feeling and you want to do it and you want to do it with the same guys who were in that dressing room."
The Canadiens also have other pending unrestricted free agents, including forwards Eric Staal, Phillip Danault, Joel Armia and Tomas Tatar; and defensemen Jon Merrill and Erik Gustafsson.
Bergevin said Friday he has not started negotiations with any pending free agent.
"There are so many important players that we brought in last year, and together with the guys we added at the deadline -- Corey Perry, Eric Staal, Gustafsson, Merrill -- they all played an important role," Montreal general manager Marc Bergevin said. "I truly think that to be successful in the playoffs, you need to have a team. A team is 23 players, 20 players in a game. So you can't talk about one single move that made the team. You have to give credit to our group, and I think the guys would tell you how much team spirit we had. We had players who wanted to work hard for each other. That's how we were successful."
Staal, acquired by the Canadiens in a trade with the Buffalo Sabres on March 26, scored three points (two goals, one assist) in 21 regular-season games and eight points (two goals, six assists) in 21 playoff games. Staal said he and his family will discuss future possibilities over the summer.
"It's not just about what I want, it's about what makes sense for us as a family with my wife and boys," Staal said. "We'll see, but my overall experience obviously, this run, these playoffs, was special. It meant a lot to me.
"It was a treat to be able to come to the arena every day and don the Habs colors and play with these guys."
Danault scored 24 points (five goals, 19 assists) in 53 regular-season games and four points (one goal, three assists) in 22 playoff games. He scored 47 points in 71 games last season but then slid on the depth chart during the playoffs to third-line center behind Nick Suzuki and Jesperi Kotkaniemi.
"My role had changed, but I was also scared that [Suzuki] and [Kotkaniemi] were going to take more minutes," Danault said. "I think we saw around the League, that if you win, you need three really good centers, like the [New York] Islanders do, like we did. It just shows you need a lot of centers to win and good two-ways as well. So, it played a role, but I found my game. I know how I am, I know what I can give, I know what I bring to a team and I know I can win."
Danault often played against the opponent's best offensive line.
"Phil's been good for us, but there are also four other players on the ice," Bergevin said. "We value Phil a lot, we did back in September, and I still hope we'll be able to get something done. But that's part of the business I don't discuss, but we value Phil quite a bit, yes."
Armia scored 14 points (seven goals, seven assists) in 41 regular-season games and eight points (five goals, eight assists) in 21 playoff games. He said he won't ponder free agency until he returns to his native Finland.
"Yeah, I'm not going to close any doors," Armia said. "I want to go home, have a little rest and think about it after I get home."
