Warren added Joshua had asked for an additional $5m on top of the multi-million offer already on the table.
Joshua is slated to fight Usyk in spring after losing to the Ukrainian in September which resulted in him losing his belts.
Fury had wanted his compatriot to allow him to fight Usyk in a unification bout first but talks fell apart.
Warren told talkSPORT Fight Night: “When Joshua asked for an extra $5million, he said, ‘Enough is enough,’ and that was it.
“He said, ‘I’m not interested, he’s too greedy,’ and that was enough. He’s a champion – Tyson’s not beholden to Anthony Joshua. Him and Usyk wanted to get it on, both of them wanted to get it on.
“But you had two people in the middle – one was suing the WBC and the other one was asking for more and more money.”
Fury publicly called Joshua greedy in a tweet when it was reported negotiations had stalled as he and Dillian Whyte had asked for more money. Whyte is scheduled to bout Fury in early 2022.
The fight would be Fury’s first since he defeated Deontay Wilder in October to retain his WBC title.