The Toronto Star said Shanahan's resignation could come as early as Friday to take a senior management role with the club.
This season, the Maple Leafs appeared headed for a second straight trip to the Stanley Cup Playoffs, but an eight-game losing streak which began in mid-March severely hurt their chances. Toronto was eliminated on Tuesday, when it lost 3-0 to the Tampa Bay Lightning, and has made the playoffs once in the past nine seasons.
Shanahan, 45, scored 656 goals and was a member of three Stanley Cup-winning teams during a playing career that earned him a spot in the Hockey Hall of Fame. He is the only player in NHL history with more than 600 goals and 2,000 penalty minutes in a career.
He retired in November 2009 and joined the NHL the next month as vice president of hockey and business development. Shanahan succeeded Colin Campbell as head of player safety in June 2011.