The heavyweight kings have agreed to a unification showdown and Arum hopes that a location for the bout is decided in the next week.
A country in the Middle East is likely to host the much-anticipated fight but Fury's US promoter confirmed that Wembley Stadium is also on the table.
Arum told Sky Sports News: "I'm very optimistic the fight is going to happen.
"Both fighters have agreed to do the fight, the question is the site and we're talking to the Middle East because allegedly they're going to come up with the biggest purse ever in boxing history.
"And if they do, that's where the fight is going to go because money is money. If they don't, both fighters will agree to do the fight this spring at Wembley... but the fight will happen in my opinion, certainly within the first four months of the year."
The Middle East has caused controversy as a leading boxing venue but Arum claims that the money on offer for the fighters is too good to turn down.
He said: "Fighters want to do the best for themselves because a fighter's career, no matter how great he is, is limited and they want to make as much money as possible.
"So that's the only issue - where will the fight be held? I would believe in the next week that will be determined and then we'll have an official announcement of the date and site for the fight - but that fight is happening."