WBC champion Fury has teased a big announcement for several weeks after an undisputed fight with Oleksandr Usyk fell through in March.
The Briton has been linked with several fighters including MMA’s Francis Ngannou and Jon Jones.
Warren told 5 Live Boxing: “I’m hoping in the next week or so we’ll be in a position to announce something.”
He added the announcement could be “a game-changer for the sport”.
Fury, 34, has faced criticism for failing to agree terms for a fight with WBA (Super), WBO and IBF champion Usyk earlier this year, with the bout appearing to fall apart over a disputed rematch clause.
Usyk is now set to defend his titles against his WBA mandatory challenger Daniel Dubois. Warren, who promotes Dubois, says that fight is pencilled in to happen in Poland on 26 August.
With Deontay Wilder and Anthony Joshua also in protracted talks over fights including with each other, heavyweight boxing has stagnated with all the biggest names stalling on making the biggest bouts
Heavyweight Joe Joyce was involved in one of the most thrilling heavyweight contests in April against China’s Zhilei Zhang and has already announced the rematch for 23 September in London.
“Are we fighting, are you not fighting? Is there undisputed or not? Just get the fights please,” Joyce said of his fellow heavyweights.
“The fans are missing out. I am the only one who seems to be fighting these days.”
Huge offers from Saudi Arabia have turned the heads of many fighters including Usyk and Joshua, and Warren says money is the main reason the big fights have not happened.
“The main reason is the market is good in some ways and not good in other ways,” Warren said.
“There are these offers being made from the Middle East, Saudi.
“That’s made people sit back and wait rather than engaging in big fights right now, with what would be a realistic price rather than the premium they’d pay to bring them over there.
“That’s the real truth. And contrary to what everyone says, Tyson and us have been trying to make those fights in the UK.”