Marner is still without a contract and previously said he "probably" wouldn't attend the team's training camp, which begins Sept. 13, without a new deal in place.
Maple Leafs general manager Kyle Dubas had positive talks with the 22-year-old's agent, Darren Ferris, in a meeting last week, according to TSN's Darren Dreger.
The maximum salary in the National League is 450,000 Swiss franc (approximately $460,200), according to 2112 Hockey Agency. Fellow Maple Leaf Auston Matthews spent his draft season with Zurich before Toronto selected him first overall in the 2016 NHL Draft.
Marner is coming off a breakout season in which he recorded a career-high 94 points and is part of a deep class of restricted free agents who are reportedly waiting for him to set the market before signing deals with their respective clubs.
Though the Maple Leafs are currently above the $81.5-million salary cap, they can build a roster with a projected cap hit up to $92.05 million before placing Nathan Horton and David Clarkson on long-term injured reserve in order to become cap compliant, according to CapFriendly.