With the Canucks officially eliminated from playoff contention after their 3-0 loss to the Anaheim Ducks on Monday night, both Gillis and Tortorella could be ousted before the season comes to a close.
Canucks ownership is looking to retool its organization, as well as its roster, and changing the club's overall system could be the first step.
Multiple sources have indicated to TFP that Gillis could be let go, altogether, and not retain his title as President of the franchise.
It is believed, as first reported by TSN's Darren Dreger, that former Canucks captain Trevor Linden is expected to join the organization. It is unconfirmed, at this point, what role Linden will have, though it's believed he could become the team's new President.
However, Linden told Global TV on Tuesday, shortly after the report, that he has not yet been approached by the Canucks about taking over as President.
In an interview on the Bro Jake Show on Team 1040 in Vancouver last week, Gillis revealed that his job could be on the rocks.
"I'm not sure if I'll be back next season," he admitted, at the time.
Whispers started to get louder over Gillis' possible dismissal following Monday night's game, where fans began chanting "Fire Gillis" towards the end of the match.
Gillis, the 10th GM in the history of the Canucks, led the team to Northwest Division titles every season since joining the organization, prior to this season, and captured the Presidents' Trophy in 2010-11 and 2011-12.
Named the 2011 GM of the Year, Gillis built a Western Conference championship team that year, setting a franchise record with 117 points in the regular-season.
If Linden is brought on as the club's new President, he will then be responsible for hiring a new GM, who will determine the fate of Tortorella.
The club's new GM will also decide the futures of stars Ryan Kesler and Alexander Edler, both of whom were almost traded prior to last month's trade deadline.
It was initially believed that Kesler and Edler would be moved in the off-season, as talks with teams would resume after the season.