Fury believes fighting the Game of Thrones star, who once weighed 31st and specialises in popping rivals' skulls (when he's the Mountain), would be 'a bit of fun'.
The pair have both announced that talks are ongoing and the fight is pencilled in to be staged at a London football stadium in November later this year.
Despite Fury claiming he has retired from professional boxing, the 33-year-old is yet to give up his WBC title belt and many still expect him to fight the winner of Oleksandr Usyk's rematch with Anthony Joshua in August.
"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."
Meanwhile Bjornsson believes he would probably lose in the fight, but he wouldn't be that bothered about the result.
Bjornsson told iFLTV: "I know that there are some negotiations going on and some talks, but nothing is complete.
"It would be a huge honour for me to fight the best heavyweight boxer in the world and it would be an amazing experience for myself.
"Would I get beat? Probably, but I would not give a f**k.
"I would do my best and who f**king knows? I'm f**king strong and my punches hurt so if it would happen he can't take it easy because I'm a warrior, I'm a Viking, and I'm going all in if it happens."
"If it would happen, I would gladly step into the ring and I would gladly fight him.
"I've said that since day one. When people have asked me 'would you fight Tyson Fury?', I've always said yes."