The YouTuber-turned-boxer is coming off the best win of his career as he beat UFC great Anderson Silva on points over the weekend.
Paul knocked down Silva in the last of the eight rounds to make his points win more conclusive. The bout was scored 78-73, 78-73 and 77-74 in favour of the social media star.
After the result against Silva, Fury moved quickly to call out Paul, suggesting on MMA Hour with Ariel Helwani that this fight would sell 70,000 tickets if it took place in the UK.
Paul appeared later in the broadcast and he claimed that Fury would be "an easy fight".
"Yeah, I love going to those crowds because they all boo me, and I shut them up. I like playing the role of the heel, especially in the UK."
He added: "Yeah, there's definitely interest, I think if his team is taking the financial risk and putting the event on then I'm cool. I just don't want to take that risk because I think he's going to back out again, most likely.
"It's an easy fight for me, the kid's a novice, he's never even fought anyone good, he's never even had an eight-round fight, he doesn't have the experience I have which is crazy to say because he's been boxing his whole life.
"But people call him a professional boxer and they respect him as a professional boxer, and I'd love to strip that title from him. I wouldn't even have to train for that fight, I would still train because I'm a professional, but I wouldn't have to train to beat him."
Paul does not have too many admirers in the boxing world as he is embracing his role of pantomime villain.
But even his haters must admit that he is gradually proving himself in the boxing world, with his win over Silva being his biggest statement victory to date.
Many had Silva as the favourite for that clash as he has previously gone the distance with Julio Cesar Chavez Jr and knocked out Tito Ortiz.
Paul impressed to beat Silva, but one thing he is yet to do is beat a legitimate professional boxer who has dedicated his life to the sport.
Fury would be an ideal next opponent in that sense, and it would garner more interest in the UK than the United States.
Tyson's brother has not exactly set the world alight so far either so you would fancy Paul to continue his momentum against the inexperienced pro.