Joshua beat Bulgarian Kubrat Pulev last month to retain his IBF, WBO and WBA titles to set up the prospect of a mouth-watering clash with fellow Briton Fury who holds the WBC belt.
“The deal is done, really – without being signed,” Hearn told The Times.
“The financial elements of the deal are done. We’re talking through the broadcast situation, the only thing really now is to paper it.
“And when you paper a deal like that, it does go back and forwards 15 times before every single letter is approved on the document.”
Fury has not fought since beating American Deontay Wilder in their Las Vegas rematch in February to claim the WBC crown.
Hearn said Joshua and Fury would face off in two fights – with the first likely to be in the Middle East later this year — and he hoped to bring the rematch back to Britain.
“The Middle East will be aggressive and will be front-runners in this. To stage this fight, you need significant government support. You need someone who is staging this fight as a statement for their country,” Hearn added.
“I’d like it (the rematch) to be (in the United Kingdom). Where? Millennium Stadium.”
