Discussions between the two sides are in the infancy stages, Mirtle notes.
Thornton, 41, is coming off his worst statistical output since he was 18 years old, as he tallied 31 points in 70 games with the San Jose Sharks. Though Thornton had hoped for a move from the Sharks to a contender at the trade deadline, nothing materialized.
The Leafs reportedly tried to persuade Thornton to come to Toronto in the 2017 offseason when the club signed Patrick Marleau, but Jumbo Joe re-signed in San Jose.
The addition of Thornton would give the Leafs some added depth down the middle of the ice and potentially allow Alexander Kerfoot to play on the wing in the top six instead of centering the third line.
Thornton, who sits 14th on the NHL's all-time points list, would undoubtedly provide some quality veteran leadership, too.
The Leafs are tight against the cap, but they could likely afford Thornton without moving anyone off their roster if he's willing to take $1 million or less.
The St. Thomas, Ontario, native is still without a Stanley Cup in his decorated career. Toronto has not won a playoff series since 2004, however.