BBC reports the bout was pencilled in for April 29 at Wembley Stadium and Usyk had agreed a 70/30 purse split in Fury's favour.
But the terms for an immediate rematch have proved a sticking point, with Team Usyk set to walk away.
Warren said he was hoping to rescue the fight during further talks with Usyk's promoter today.
Representatives for unified champion Usyk say they have done everything within their power to make the bout happen.
"I've sent [Usyk's promoter Alexander Krassyuk] a message and I've had one back. We're going to speak in a couple of hours' time," Fury's co-promoter Warren said.
"I want the fight to happen. It's a very important fight for boxing, it's an important fight for Usyk whose dream is to unify the titles and it's an important fight for Tyson to go and do what he set out to do."
Both parties still have until 1 April to agree a deal after the WBA said it would wait until that date before ordering Usyk to fight mandatory challenger Daniel Dubois.
When Fury, 34, beat Derek Chisora in December to retain his WBC title, he said agreeing a deal with Usyk and his team for an undisputed fight would be easy - but that has not proven to be the case.
After months of back and forth, Fury publicly declared 12 days ago he would not accept anything less than a 70/30 purse split in his favour.
Usyk surprised everyone by accepting that offer, despite holding three of the four world titles, and subsequently informed governing body the WBA that terms had been reached.
However, Fury then said he would not sign any deal that included a rematch clause.
Photo: PHOTOSPORT Caption: Oleksander Usyk