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The WBC world heavyweight champion was named after the Baddest Man on the Planet, who became champion aged just 20 and ran riot in the division in the late 80's.
But Fury, who is 31-0 in his career, says no heavyweight in history, including Tyson, would have been able to hang with him.
He made the claim whilst watching back his stunning win over Deontay Wilder in February and listed five reasons why none of the greats could have beat him.
"There isn't a heavyweight from any era in the last a thousand years that could've tackled me or beat me," Fury responded on BT Sport's 'What Went Down' when asked by Steve Bunce if he would have relished the challenge from 'Iron' Mike.
"Never mind Mike Tyson from the 80s, Muhammad Ali, Joe Louis, Lennox Lewis, George Foreman, Ken Norton, Rocky Marciano, Floyd Patterson, Gene Tunney, Jem Mace, John L. Sullivan.
"Going right back to the beginning, not one of them could've beat the Gypsy King. I'm too big, I'm too good and I've got too many styles for them. I'm an adapter and they couldn't even beat me anyway.
"I'm the greatest fighter that has ever lived. Never mind heavyweight, greatest fighter that's ever lived. How about that for a bit of modesty?!"
Fury's dad John, who has also called out Tyson for a fight in recent times, absolutely lapped it all up.
The 55-year old has even claimed he's in better shape than heavyweight legend Tyson despite the Brooklyn fighter looking in incredible physical condition as he prepares to take part in some exhibition bouts.
But it's current world champion Fury Jr who has reportedly been offered to step inside the ring with Tyson, though it likely won't materialise according to the man himself.
"I did get a phone call with a chance to fight Mike Tyson. I was like 'what?'" Fury told BT Sport last month.
"Yeah, I had a phone call saying 'would you like to fight Mike Tyson in an exhibition fight?' I was like 'hell yeah!'
"But I don't think anything's materialised out of it to be honest."
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