The two world heavyweight champions went face-to-face ringside after Fury beat British rival Derek Chisora on December 3.
Arum has now revealed that he is waiting for an offer from Saudi Arabia to stage the fight in the Middle East.
The veteran promoter has given them until the end of this week to come forward. If they don't, he has indicated that Wembley is the next most likely venue for the undisputed bout, but "talks about percentages" would need to take place.
"The fighters have agreed to fight," Arum said.
"I spoke to Frank Warren. We're giving them until [this] week to come with their offer, which I believe we'll get.
"If we don't, then we're gonna do the fight at Wembley. And then we'd have to talk about the percentages because Usyk wants 50-50.
"That's not right if the fight's at Wembley because there will be 95,000 Brits at the fight and big Brit pay-per-view money, so Tyson deserves the lion's share.
"But we don't get to that point if the [investors in Saudi Arabia] come through, because the way they operate is they make deals with each of the fighters.
"We've been led to believe that they're going to come with a proposal [this] week. I'll believe it when I see it, but it's not like they haven't come through in the past."
It's hard to believe anything that comes from Fury or his team after the mess that was talks with Anthony Joshua last year.
A lot of work is to be done for Fury-Usyk to be agreed, with World Boxing News reporting that an agreement is 'nowhere near'.
'A final draft of the paperwork isn't ready' despite the bout being pencilled in for March/April.
The report adds that that 'hold-up stems from a trio of events', which are the fight venue, purse split and 'dates in the Pay-Per-View calendar'.