Fury offers Joshua 'Battle of Britain' heavyweight bout
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Fury, who suggested he was retiring from boxing after beating Dillian Whyte in April, is now searching for a high-profile opponent after rival champion Oleksandr Usyk said he does not intend to fight again until 2023.
Joshua suffered a second consecutive defeat to the Ukrainian in Saudi Arabia last month and his promoter, Eddie Hearn, is considering options for a return early next year.
Fury announced he was retiring on his 34th birthday last month, having previously performed a number of U-turns over his future in the sport.
But in a video posted on social media on Monday he appeared to confirm he had reversed his decision.
"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," said Fury.
"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. Let me know if you're interested. If not, I will select another opponent."
Joshua is unlikely to take the bait as his team look to help him rebuild with a bout against a different opponent.