Contract talks between the Maple Leafs and Kessel picked up this month and intensified over the last few days.
Kessel, 25, is expected to sign the new deal on Tuesday, at some point before the Leafs' first game of the season in Montreal against the Canadiens.
In 48 games with the Leafs last season, Kessel registered 20 goals and 32 assists for 52 points.
The native of Madison, WI, has played in 504 career NHL regular-season games with the Boston Bruins and Leafs and has accumulated 185 goals and 194 assists for 379 points.
Kessel, drafted fifth-overall by the Bruins in the 2006 NHL Entry Draft, was traded to Toronto on Sept. 18, 2009, in exchange for two first round draft picks and a second round pick.