The promoter has been working on another fight between the heavyweight stars after a court ruled that Wilder is entitled to a third fight before Fury can turn his attentions to a unification clash with Anthony Joshua.
Arum told reporters: "We’re finishing the paperwork. July 24th is the working date. Hopefully, we can get it done today. All of the terms are spelled out in that old rematch clause that we had in the original [two-fight] deal. There was very little work to do, almost nothing. It was a two-page document."
Arum admitted the verdict that Fury must have a third bout with Wilder came as a "gut punch" with a fight with Joshua so close but has come to terms with the decision.
He said: "It was a real gut punch. But luckily, I’m a little sophisticated, so I know if you have a case where you’re 100 per cent sure of winning and you don’t get the win, it can happen. I mean, the decision I think is incomprehensible. But again, we lost. And therefore, we’ve gotta make do."
Fury knocked out Wilder during their rematch last year but Arum says the result of the new clash isn't a foregone conclusion.
He said: "Based on the last fight, it should be a relatively easy fight for Fury. But you know in boxing, particularly with the heavyweights, this next fight could turn out different."