It would be Joshua's second fight in the kingdom. He reclaimed his WBA, IBF and WBO belts from Andy Ruiz there in December 2019.
Joshua's only fight since saw him retain his titles by knocking out Kubrat Pulev in December.
Fury hasn't fought since beating Deontay Wilder in February last year to capture the WBC title.
Fury and Joshua have called each other out over Twitter over the last 24 hours, both urging the other to finalize terms for the fight.
Hearn said the "deal is done" but there was frustration on both sides that the fight had not been officially announced.
"From our perspective and AJ's perspective, we're ready to go," he said. "From Tyson Fury's perspective, they've got a couple of lawyers across it from their point.
"We have to nail this," Hearn added, "and I'm not going to stop until I nail it, and everyone has just got to move forward collectively. We're ready to go from our side. We're not far away from their side and it is inevitable."