The 23-year-old forward can become a restricted free agent July 28.
"I hope I can stay in Columbus," Laine said in remarks published by Aamulehti in Finland on Tuesday and translated by NHL.com. "This is the starting point, but you can never be sure what happens. I got traded once."
Laine was acquired by the Blue Jackets with forward Jack Roslovic from the Winnipeg Jets on Jan. 23 for forward Pierre-Luc Dubois and a third-round pick in the 2022 NHL Draft. Laine scored 21 points (10 goals, 11 assists) in 45 games after the trade.
"I really haven't thought about the contract negotiations," Laine said. "At some point they will let me know what the situation is, and they will ask what I think about this proposal. Do I want to take the contract? And then we continue (the negotiations)."
Larsen was named coach of the Blue Jackets on June 10. The 44-year-old replaced John Tortorella after it was announced May 9 he would not return after six seasons. Larsen was an assistant under Tortorella and former Blue Jackets coach Todd Richards for seven seasons and coached Springfield of the American Hockey League from 2012-14.
"He knows what he's doing," Laine said. "It's hard to say what he will be as a head coach because he never has been a head coach in NHL. Let's hope he refreshes us."
Laine admitted he did not agree with Tortorella's philosophy about his role in Columbus. The No. 2 pick in the 2016 NHL Draft scored 0.46 goals per game with the Jets (140 goals in 306 games) and 0.22 with the Blue Jackets. He scored at least 28 goals in each of his first four NHL seasons, including a career high 44 in 2017-18, second in the NHL behind Washington Capitals forward Alex Ovechkin (49). Laine was runner-up to Toronto Maple Leafs center Auston Matthews in voting for the 2017 Calder Trophy as NHL rookie of the year.
"I scored lot of points in that span," Laine said. "It would be stupid not to use this potential. But what the coaches think, that's a totally different thing.
"Forwards wants to play an offensive style of hockey. If you want to score, you need to take some liberties. This is not possible if the coaches think a different way. I understand the tight strategy, but every player is different. I don't want to be same kind of player like everyone else. I am what I am, and I do things my own way. Everyone should be allowed to be what they are, but of course you have to stick with the team system."
The Blue Jackets (18-26-12) tied the Detroit Red Wings for last in the eight-team Discover Central Division this season. It was the first time Columbus missed the Stanley Cup Playoffs since 2015-16, Tortorella's first season as coach.
"It wasn't easy season for me nor the team," Laine said. "The last weeks were rough when the playoff spot wasn't available anymore. I didn't think about hockey after the season, and still haven't. I was just happy that I didn't need to play anymore."