Leafs GM Dave Nonis had dangled Kulemin as trade bait earlier this season, but opted against dealing him.
Kulemin, 27, is in the final-year of a two-year, $5.6 million contract.
In 67 games with the Maple Leafs so far this season, Kulemin has registered nine goals and 11 assists for 20 points.
It has been widely speculated for years that the Pittsburgh Penguins could try to sign Kulemin this July, if he hits the open market as an unrestricted free agent, as his friendship with Penguins star Evgeni Malkin has played a role in the rumors.
It seems unlikely that Kulemin will look to sign overseas in the Kontinental Hockey League, and several NHL clubs will express interest this summer.
If the Leafs do not, in fact, re-sign Kulemin, it will be one of many moves the team will be making this off-season.
Maple Leafs goaltender James Reimer, a pending restricted free agent, and center Nazem Kadri are both expected to be traded.
The Leafs will aim to re-sign UFA-to-be forwards Dave Bolland, Mason Raymond, Jay McClement and Troy Bodie.