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Fury, 33, has not fought since announcing his retirement from professional boxing in April after defending his WBC heavyweight title against Dillian Whyte at Wembley.
'The Gypsy King' is now set to make his comeback against Bjornsson, who played 'The Mountain' in HBO's Game Of Thrones, with negotiations underway for a fight to be staged at a London football stadium in November.
"It would be a bit of fun," Fury told The Telegraph.
"It would be great to get in there in front of, say, 70,000 fans and show him what boxing is all about, make him miss, and knock him out.
"We are talking to his team at the moment and it is definitely something I'm interested in."
Fury is yet to relinquish his WBC title and hopes remain he will return to professional boxing to face the winner of Anthony Joshua's upcoming rematch with Oleksandr Usyk.
Usyk will defend his WBA, WBO and IBF belts against Joshua in Jeddah, Saudi Arabia next month.
However, Fury has dismissed the prospect of facing the winner in an undisputed title fight.
"I'm not overly concerned with Anthony Joshua and Usyk in Saudi Arabia next month, whoever wins, because I've achieved everything I wanted to as a professional boxer, undefeated and having won all the belts," he added.
"There are so many other things I can go on and do."
Icelandic giant Bjornsson made his boxing debut in 2021 and now holds an unbeaten record of 2-0-2.
He most recently beat former strongman rival Eddie Hall via unanimous decision in March, in a fight dubbed 'The Heaviest Boxing Match In History'.
Bjornsson, who was ringside at Fury's victory over Whyte, has also confirmed talks are underway for a fight against the world heavyweight boxing champion.
"I know that there are some negotiations going on and some talks, but nothing is complete," he told iFL TV.
"If it did happen, I would gladly step into the ring and I would gladly fight him."
Speaking ahead of his win over Hall, Bjornsson revealed he was studying Fury to help him prepare for the fight.
"There's a lot of guys that I look up to. Lennox Lewis, Tyson Fury… many, many others that are active today," Bjornsson told SPORTbible.
Featured Image Credit: Alamy & Instagram/thorbjornsson & Instagram/tysonfury
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