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Fury retained his WBC world title with a victory over Dillian Whyte at Wembley in April and stated that was his last fight.
The Brit appeared to backtrack this month by stating he would be returning to the ring and wanted to face Dereck Chisora for a third time, having already been victorious over his compatriot in 2011 and 2014.
Fury then announced once again that he has retired in a social media post on his 34th birthday last week.
Joshua and Usyk will do battle once more this weekend in Saudi Arabia, after the former undisputed cruiserweight champion took the Brit's IBF, WBA and WBO belts with a unanimous decision victory at Tottenham Hotspur Stadium last September.
Arum believes the 'Gypsy King' can be tempted back into the ring to face whoever comes out on top.
He told Sky Sports: "Absolutely - it's really the only fight that makes sense for Tyson Fury.
"I've discussed this with my co-promoter of Fury, Frank Warren, and once this fight is over we're going to put together a total unification match between the winner and Tyson Fury.
"Now, if Usyk wins the fight, which I expect, that will be quite easy to do because we're very close to the Usyk people as they're the same people who manage Vasyl Lomachenko who fights for us. If Joshua wins, Eddie Hearn is his promoter. We've talked many times with Hearn about various matches and I'm sure we'll be able to come together on this one.
"I've talked with him [Fury] and every day is different, but he's a fighter and if the right fight is there then Fury will be up for that fight. The right fight is the unification fight against the winner of Usyk and Joshua and I think - based on my conversations with Fury - he'll be up for that challenge.
"How much longer he will go after that, god only knows and I'm not sure, but I'm confident at least that he'll answer the bell for that major fight."