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Usyk produced a stunning performance to beat Anthony Joshua by unanimous decision and captured the WBA (Super), IBF, WBO and IBO titles.
The 34-year-old Ukrainian star will have to face former champ AJ in a rematch before turning his attention to a potential unification clash with Fury.
Meanwhile, Fury closed the chapter on his memorable trilogy of fights with Deontay Wilder after his sensational 11th-round knockout win on Saturday.
The 33-year-old Brit superstar is expected to face either interim champ Dillian Whyte or Otto Wallin next if the WBC enforces a mandatory challenge.
Big John now claims that his son “fears no man” and will be going after “those other belts and Usyk.”
Speaking to The Daily Mirror, Fury's father said: “Usyk is more scared of Tyson than you will ever know because he knows how good he is.
“It’s all about what AJ does next, does he go straight into the rematch with Usyk?
“Tyson doesn’t care who’s next and he’ll fight anyone. He fears no man because he knows he has the beating of them all.
“He’s said he’d love to fight again this year against Dillian Whyte or whoever is out there. He’s going to go after those other belts and Usyk.
“He had those three belts before he had to give them up because of his problems. He never lost them in the ring and he regards them as his.
“He wants them back and he will fight Usyk or Joshua, whoever he needs to get them.”
Whyte could finally land his long-awaited title shot should he successfully defend the WBC interim title against Wallin on 30th October at the O2 Arena.
Fury, who hasn’t fought in the UK since his win over Francesco Pianeta in 2018, has hinted that he would love to stage a homecoming fight at Old Trafford.
Matchroom chief Eddie Hearn has confirmed that Joshua has invoked his rematch clause and will face Usyk sometime in early 2022.
“He’s got his head back in the game, he’s training now and today we officially triggered the rematch for the Oleksandr Usyk fight, which we’ll see early next spring,” he told DAZN on Saturday night.
“Back in the game and looking for him to become a three-time heavyweight world champion.
“That’s officially triggered now and we’ll sit down with K2 [Usyk’s promoters] to plan the dates for that.
“I think realistically March is when you’re likely to see the rematch.”
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