The Calgary Flames, Dallas Stars and New York Rangers each have a coaching vacancy.
Peters, 53, was 137-138-53 in four seasons with Carolina and failed to make the Stanley Cup Playoffs. Carolina was 36-35-11 this season, 14 points behind the New Jersey Devils for the second wild card into the playoffs from the Eastern Conference. The Hurricanes have not made the postseason since 2009.
Peters said the decision to step down in Carolina was not one taken lightly. He had one year remaining on his contract and an opt-out clause he needed to exercise by Friday.
"It's something I had to think about, for sure," Peters told the paper. "Game 82 hits and you're used to going a million miles an hour and you're going, going, going and all of a sudden you have no games, no practices. ... It takes awhile to decompress, and look back and try and give it a little bit of time and look back with clear vision. I think we were able to do that.
"It kept coming back to the fact that a new [general manager] deserves the opportunity to hire his own coach. And especially when you combine it with a new owner and a new GM, I think they need to chart their own path."
Tom Dundon took over as majority owner of the Hurricanes on Jan. 11 and reassigned former GM Ron Francis, who remains with the organization. Carolina does not have a GM.
"Tom and I met four or five times," Peters said. "It was excellent. He's a guy who has been successful in business. Owning and managing a sport team is a business. No reason why he can't be successful again."
Peters will coach Canada at the 2018 IIHF World Championship. He won gold as Canada's coach at the 2016 tournament.
"Really a great area, with great people in the community," Peters said of his time in Carolina. "I worked with a ton of great people. I'm thankful for the effort from the players in our four years. I'm thankful for the fans' support. They're very passionate fans. ... It's all positive memories for me, it really is."
