Price, who will turn 30 before the start of next season, has one year left on his contract and can become an unrestricted free agent July 1, 2018. He is eligible to sign a new contract July 1.
"Yeah, of course," Price said when asked if he would be open to starting negotiations on his next contract. "I love playing here. I'm sure we'll figure something out."
Price is entering the final season of a six-year, $39 million contract he signed July 2, 2012, according to CapFriendly.com. It was one of the first things Bergevin did after he was hired May 2, 2012. He seemed confident Monday that Price would arrive at training camp in September with a new contract signed.
"It's a possibility, a strong possibility," Bergevin said. "We have to make something work. I can't negotiate with him now."
The alternative would be to have Price enter the final season of his contract as an impending free agent, something Bergevin clearly did not want to see happen.
"We'll cross the bridge when we get there," he said, "but obviously it would be a big issue if he doesn't (sign)."
The thought of Price not signing a contract during the offseason could lead some to think the Canadiens should trade him before next season so they don't lose him for nothing. It would also allow Bergevin to fill what is a giant hole at the center position, especially since Bergevin said Monday that Alex Galchenyuk is likely to play on the wing next season.
Bergevin quickly put to rest the notion that Price might be traded in the offseason.
"I never talk about trades, but I'll tell you," Bergevin said. "No."
Price's next contract will determine what Bergevin can do to improve the Canadiens. With an average annual value of $6.5 million under his current contract, it could be said that Price has been a bargain over the past few seasons, having been one of the best players in the NHL.
Price went 37-20-5 with a 2.23 goals-against average, a .923 save percentage and three shutouts in 62 games during the regular season and is a finalist for the Vezina Trophy awarded to the top goalie in the NHL. He won the Vezina and Hart trophies in 2015. In 509 regular-season games over 10 seasons, Price is 270-175-55 with a 2.40 GAA, a .920 save percentage and 39 shutouts.
Price seemed to suggest he hoped his contract wouldn't cripple the Canadiens' ability to build around him.
"That's part of the business," he said. "That's a tough question to ask me right now. I want to stay here. I know we'll figure out a way to make all the pieces fit and bring a championship here."