The British heavyweights now hold all of the division’s belts between them, after Fury secured a knock out win against Deontay Wilder, 34, to claim the WBC title.
Joshua’s promoter Eddie Hearn said “let’s give the fans what they want”.
And Warren told BBC Sport: “Of course we want to see the fight. We’ve been trying to make it for two years.”
“Hearn kept saying was it’s got to be 70/30 [the purse] in favour of AJ and so on and so forth.
“The tables have turned now. I have no problem with 50/50. I think Tyson would deserve more but 50/50, no problem.
“This is about the boxers and more importantly the fans. If they want to see the fight we will make it happen.
“In the meantime Eddie Hearn is acting like the guy standing outside your house with his nose pressed up against the window and keeps spouting off about Tyson.”
The immediate prospect of the fight now relies on the fact Wilder has the option of a rematch with Fury and has 30 days to invoke a clause in his contract.
Hearn says if that happens then Joshua, 30, will face Kubrat Pulev in a mandatory IBF bout, with the promoter in talks to hold the fight at Tottenham Hotspur Stadium on 20 June.
Hearn told BBC Radio 5 Live: “The fight we want more than anything is the undisputed fight. The person that holds the key to that is Tyson Fury. If we can get that next we are all in on that fight.
“I think 50/50 is a very straightforward deal. Frank’s going to have his views but it’s a pretty straightforward deal. Joshua is the bigger commercial draw.”
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