The iconic American memorial situated in the Black Hills of South Dakota features the carved heads of former US presidents George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.
Top Rank boss Arum was asked to name which fighters can consider themselves lucky enough to feature on his very own Rushmore.
But speaking to The Rich Eisen Show, Arum explained why he believes 31-0 Fury is the greatest heavyweight of all time.
When asked who would in a fight out of a prime Ali and Fury, he replied: "Fury wins. No heavyweight, no heavyweight before or since could beat Fury. Fury is so incredible.
"Guys were 6 ft 9 were bums when Ali was fighting right because they couldn't move and there were always flaws.
"But here's a guy Fury [who] takes an incredible punch, moves like a welterweight, and has a pretty good punch himself, knows how to box. We haven't seen that combination ever, ever.
"You know, I feel sorry for [Deontay] Wilder who's a terrific fighter because he came in an era that gave us Tyson Fury, and remember it's not a fluke because Tyson Fury beat Wladimir Klitschko when Klitschko was riding high and nobody gave Fury a chance.
"Fury is the goods because he can box, he can punch, and he keeps getting better."
However, Arum neglected to even mention Mayweather during the conversation, who suffered the ignominy of once again being overlooked by his former promoter.
Two of the sport's most powerful figures have a notoriously strained relationship, with their fair share of ups and downs over the years.
In 2006, Mayweather split from Arum for good after he defeated Zab Judah in order to pursue other opportunities elsewhere as a free agent.
However, Arum has insisted he never had any issues with Mayweather. His biggest problem, he says, came in the shape of Mayweather's advisor Al Haymon.
Haymon, who set up Premier Boxing Champions that is broadcast live and free to air on NBC, CBS, SHOWTIME, Fox Sports and Spike TV among others, has become one of his biggest competitors.
"I never had any animosity with Floyd the whole time he was with us, and I didn't have any after he left," he told Yahoo! Sports in 2015.
"It was all Haymon. Here's what you have to understand about Haymon. He works to manipulate things.
"So when Floyd started talking and saying things, yeah, the mouth was Mayweather but the words were Haymon. That's how he operates."
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