The all-British heavyweight showdown would be the first fight in history in which all four heavyweight titles are on the line.
Fury, 32, is WBC champion while Joshua, 31, holds the IBF, WBA and WBO belts.
"We have a fight on our hands, and sorry to the governing bodies, that eclipses all belts," promotoer Eddie Hearn said.
"We've just got to be a bit careful because you may be on the verge of saying, 'Let's just get rid of politics right now. Let's just drop all the belts because if we lose one belt, we might as well lose them all,' he told Matchroom Boxing.