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Fury took to social media on Monday afternoon to offer Joshua a chance to fight for the WBC titles.
Fury said in a video: "You've all heard that I'm going to be fighting within the next few months, and before I announce an opponent I need to do this just in case.
"Anthony Joshua, I know you've just lost a fight to Usyk, and I know you're belt-less at the moment, and I'd like to give you an opportunity to fight me for the WBC heavyweight championship of the world and the lineal championship in the next few months.
"You're coming off a 12-round fight so you're match fit, you're ready, I'm giving you a few months' notice.
"If you're interested I'll send you the date over and we can rumble - a battle of Britain for the WBC heavyweight championship of the world."
Fury initially announced he was retiring from the sport after his comfortable win against Dillian Whyte in April, however, it looks like 'The Gypsy King' is likely to be tempted back in the ring.
And now, Joshua has replied on Twitter.
He tweeted: “Yea calm. I don’t do the online discussions just for clout, so if your really about it shout
@258mgt. I’ll be ready in December. Khalas”
Joshua recently lost the rematch against Oleksandr Usyk in Saudi Arabia, despite putting it a much improved performance, he was no match for the tricky Ukrainian. Usyk successfully defended his WBA, IBF, WBO and IBO titles.
Usyk said after his win against Joshua that he wanted to fight Fury, but he has recently ruled out a fight happening this year.
He said: "It won't happen this year, that's for sure. I'm totally healthy and don't have any injuries, but I have old traumas which have resurfaced, and which need to be treated. I will need up to two months to recuperate."
Will we see the much anticipated fight between the two Brits this year? Only time will tell.