On Tuesday, general manager Kyle Dubas said that the two sides have made progress on a new deal, according to Sportsnet's Chris Johnston. Dubas added that he'd like to get an extension done as soon as possible for long-term clarity before the Feb. 25 trade deadline.
Contract talks between Matthews and the Leafs began last July.
The 21-year-old is a pending restricted free agent in the final year of his entry-level pact. He ranks second on the club in goals (20) and fourth in points (42) despite being limited to 34 games this season due to injury.
Fellow Leafs forward Mitch Marner is also a pending RFA, but Dubas said the club isn't negotiating with Marner at the request of the winger's agent, Darren Ferris, who told The Athletic's Pierre LeBrun earlier this month that his client "100 percent" doesn't want to engage in contract talks until season's end.
Dubas insisted Tuesday that he isn't pressuring Matthews or Marner to sign quickly, but said that's his preference.
"Yes, it would be selfishly for me beneficial," the GM told reporters, according to Johnston. "But for the players, I think they have to make sure they're fully comfortable in going into any arrangement."