Joshua, 31, holds the IBF, WBO, WBA and IBO titles while Fury, 32, is the WBC belt holder.
"August the seventh, August the 14th. I think it's a very bad secret that the fight is happening in Saudi Arabia," Eddie Hearn, head of Matchroom Sport and Joshua's promoter said.
Joshua won back his belts from Andy Ruiz Jr in Diriyah, on the outskirts of the Saudi capital Riyadh, in December 2019. He had lost the belts to the Mexican-American in an earlier shock defeat.
Hearn said Fury's lawyers were going through the fine details but an announcement could come this week.