The world heavyweight champion will face Dillian Whyte at Wembley Stadium on Saturday, in an event set to be attended by 94,000 spectators, but the build-up to the all-British bout has been overshadowed.
The Irishman who has advised Fury in the past, was last week named as being head of the Kinahan drugs gang and hit with worldwide financial sanctions by the United States government, who have offered a $5million reward for information on the group leading to the arrest and conviction of its leaders.
Kinahan, who has always denied any wrongdoing, is alleged to be one of the leaders of a cartel the US authorities accuse of smuggling drugs, money laundering and bringing violence to "the most vulnerable in society".
WBC president Mauricio Sulaiman released a statement on Monday stressing "at no time" did he have a working relationship with the Irishman.
A day after US sanctions were brought against Dubai-based Kinahan, a virtual press conference took place to preview the fight at Wembley, but, with a moderator on hand to pick the journalists permitted to ask questions, Fury was not quizzed on the issue.
He did, however, address the elephant in the room after Tuesday's open workout at BOXPARK Wembley.
Asked if he had any business with Kinahan, Fury said: "Zero, absolutely zero.
“That’s none of your business and none of anybody else’s business, I don’t think. Is it?” Fury said. “My business is my business, your business is yours.
“Like I say, it’s got nothing to do with me in boxing. I’m just a stupid boxer who gets punched in the face for a living. If I wasn’t, I wouldn’t be here, would I?
“I’ve said this to quite a few people this week: I don’t get involved in other people’s businesses, and I keep mine to myself, and that’s it.
“What other people do in their own lives... I’ve got my own troubles and my own problems to work on myself with a wife and six kids, so I keep my business to myself.”
Asked if the US moves against Kinahan had been a distrction, Fury said: "Has it been a distraction? Not really, it's got nowt to do with me, has it?
"If I say, 'There's a war going on in Ukraine', and people ask me about that, it's got nowt to do with me. I keep my business to myself. I've got my own troubles to look after with six kids and a wife.
"I've got a lot more to think about than other people's business. In my life, I've got a man who wants to punch my face in next week and I've got to deal with that. Anything else is out of my control."
Quizzed on the size of the story, Fury admitted: "I don't really take any notice of the media. I know what the media can do and I was the victim of a witch-hunt in 2015 and 2016."
Fury, who is co-promoted by Top Rank, was pictured with Kinahan in Dubai in February but played down the image.
"A picture doesn't mean I am a criminal," said Fury. "I can't control who is in the building.
"There could be a criminal in this building now. It doesn't mean I am involved in his criminal activity, does it?"
Top Rank chief executive Bob Arum told Yahoo Sports last week that Kinahan had received payments for his help with the four most recent Fury fights.
On Arum's comments, Fury added: "That's Bob Arum's own personal business, what he does with his own money. He can spend it all on gummy bears if he wants to.
"What someone does with their money is out of my control."
Frank Warren, who also promotes Fury, insisted the pair had no idea about Top Rank's payments to Kinahan.
He said: "Let me make a couple of things very clear - one, Daniel Kinahan has nothing to do with this show and, two, as Tyson said, he was unaware of any payments made by Top Rank to Daniel Kinahan.
"We were unaware of any payments being made."
Warren was asked if he was concerned for boxing after the US Government told anyone with links to Kinahan, who has advised several boxers and founded promotional company MTK Global in 2012, to end them last week.
He added: "I am concerned, but I'm also concerned about some of the misinformation that's going around. We're not stupid people. All of us understand what has happened from the US Treasury.
"It's been going on now for three years and we all know what we have to do and we will not be breaking the law. By the way, we've never broken the law.
"Is it a bad image for boxing? We've sold 94,000 tickets in a day or two days. Are we going to do the business on the pay-per-view? Yes, we are.
"We're very conscious of what we have to do as participants and guardians of the sport, but we're not policemen. We're not the police. It's only after last week that it's actually come to something."