The discussions over an undisputed world heavyweight title showdown between the two fighters began in early May and they have now agreed on initial terms for two encounters.
Joshua holds the WBA, IBF, WBO and IBO belts, while Fury is the reigning WBC champion.
"We're making great progress," Joshua's promoter Eddie Hearn told Sky Sports News. "There is still a lot to overcome. We are looking at venues and dates.
"We have the Dillian Whyte mandatory which is due before this fight.