The Canucks are in a downward spiral, having won three of their last 15 games.
After trading goalie Roberto Luongo to the Florida Panthers, several months after trading netminder Cory Schneider to the New Jersey Devils, the Canucks came close to dealing star Ryan Kesler to the Pittsburgh Penguins and Alexander Edler to the Boston Bruins before the trade deadline.
It has been widely reported that both trades were nixed by Canucks ownership, who informed Gillis to follow up on those deals in the summer.
"There's a lot of rumors and speculation out there, and for me to comment on it would lend some degree of credibility to it, which is not something that's good for anybody," Gillis said.
"It's unfair to comment on any future plans, other than what we've already said, which is we're trying to get younger, we're trying to retool, and we're trying to do some things a little differently in the next one, three, five years."
Gillis would not comment on whether or not Tortorella's job is in jeopardy, but did indicate that the entire team is at fault for its long-lasting slide down the standings.
"From top to bottom, our whole team has under-performed," Gillis said. "It isn't because of a lack of effort (or) lack of caring, we've had a very tough year for a lot of different reasons."
The Canucks are expected to make several changes this off-season, with Kesler and Edler among those likely on the move.
Prior to the deadline, teams inquired about defensemen Kevin Bieksa and Dan Hamhuis, both of whom have a no-trade clause, and could revisit discussions in the off-season.
"Our message to the fans is always the same," Gillis said. "We're doing everything we can to win hockey games. We're doing everything we can to put the absolute best team on the ice.
"This is a time of transition for our hockey club, and we have to recognize that."