Canterbury chief executive Andrew Hill said that despite the speculation, the 27-year old may yet remain at Belmore.
“There has been interest expressed in Aaron via his management but to date that interest has not amounted to any significant conversations,” Hill told the Sydney Morning Herald.
“As a result of the club agreeing to Moses Mbye’s move to the Tigers, that has freed up some salary-cap space, so we’re in a position to not have any players leave to be cap compliant.”
“Everyone knows Woodsy is a great club-person, he’s a strong player and he’s great to have around the team.”
Woods has been linked to Cronulla ahead of the June 30 trade deadline, who have publicly declared their interest in the front-rower.
After signing an approximate $800,000-a-season deal with the Bulldogs, he is reportedly now valued at $150,000 a year less than that, and rival clubs are refusing to pay much more.
Fellow Bulldogs prop Aiden Tolman said Woods was an important piece for the Bulldogs.
“He’s an Australian representative” he told the Sydney Morning Herald.
“A quality person and player and a leader at this club.”