Marner said he expects talks between Dubas and his agent, Darren Ferris, to heat up in the coming days.
"It's a major priority," said Marner, who has 224 points (67 goals, 157 assists) in 241 games with the Maple Leafs. "I want to be here. I want to play for this team. I love the people in this locker room, I love the people that work in this organization. We're a tight-knit group. It's a special group to be a part of."
Babcock is halfway through the eight-year contract he signed with Toronto in 2015.
Dubas said he and Babcock, who helped lead the Maple Leafs to the Stanley Cup Playoffs the past three seasons but has not made it past the first round, talk every day during the season, whether it be about game plans, ice time for players, pretty much everything.
"We have to continue to improve everything that we do," said Dubas, who became Maple Leafs general manager on May 11. "It starts with me, improving the job that I do -- contracts, signing players, drafting players, development system, every single thing in our organization, and it's up to me to work with Mike to continue to have him improve and have his staff improve, and I think that's one of the best things about working here.
"There's not anybody staunch in their stance that what we're doing is great, and we can't change it. We know we have to improve and get better and that's the exciting part of it."
Another situation the Maple Leafs have to resolve is that of defenseman Jake Gardiner.
Dubas said he won't be able to determine if the 28-year-old, who can become an unrestricted free agent on July 1, can be signed under the NHL salary cap until Marner's contract has been ironed out.
Gardiner had 30 points (three goals, 27 assists) in 62 games this season and has 245 points (45 goals, 200 assists) in 551 games over eight NHL seasons, all with the Maple Leafs.
He played all seven games against the Bruins despite dealing with a back injury and had two assists.