The pair had fought out a controversial draw in 2018 before Fury stopped Wilder last month to clinch the WBC heavyweight title.
“He’s invoked the rematch clause so that is what we are working towards,” Warren told talkSPORT radio on Monday.
“It’s contracted to take place in the States. That is in the contract and set in stone unless anyone agrees differently. But at the moment it is due to take place in the US. It will take place by the end of June, early July – no later than that.”
Fury’s US promoter Bob Arum also told Ringside Reporter that he had been “formally notified” by Wilder and his representatives that they have accepted the new fight.
“It’s going to happen in the summer, before the Olympics. Middle of July,” Arum said.
‘I will rise again’
Wilder had 30 days to trigger the clause after his unbeaten streak was emphatically ended by Fury, dubbed the “Gypsy King.”
Fury produced a boxing masterclass to dominate the 34-year-old US fighter in Las Vegas, knocking Wilder to the canvas twice before his opponent’s corner threw in the towel in the seventh round.
Wilder, who partly blamed his defeat on a heavy ring-walk costume, said he would “rise like a phoenix” to reclaim his title.