Several media reports on Thursday say Shanahan will become the new president of hockey operations for the Leafs.
Shanahan, who was born in Toronto, played in the NHL for 22 years and was inducted into the Hockey Hall of Fame in 2013.
The 45-year-old retired as a player in 2009 and joined the NHL's executive as vice president of hockey and business development a month later.
On June 1, 2011, Shanahan replaced Colin Campbell as the league's chief disciplinarian, helping the NHL crack down on illegal plays.
Toronto is winding down a difficult season that saw the Leafs lose eight games in a row in late March to drop out of the Eastern Conference's playoff picture.
Shanahan began the use of videos to explain why players were or weren't suspended for dangerous or illegal plays.
The videos posted to the NHL's website have been used as an aid for players, fans and officials as the league tries to limit the number of concussions in professional hockey.
Shanahan's punishments have been playfully called "Shanabans," a portmanteau of his last name and the term "ban," referring to suspensions.