Arum has already made a claim that if Parker becomes champion, his next fight would be in the United States, on top of a massive fight card.
"The next logical step would be to fight in the United States on the top of the bill," Arum said.
"We would like, if Parker were to win, to have him, as the heavyweight champion, make his defence at the top of the card of championship fights."
But Arum wasn't giving Parker a sure-fire ticket. He still believes Andy Ruiz is one of the best in the world and, although stating Parker had the hardest punch in the division, said Ruiz has the skills to become the world's best as well.
Steve Bunce, a UK-based boxing analyst and columnist, suspects Arum might be talking up Parker's fame because of his promotional background, however, in this instance he agrees with Arum's claims that the winner will have a legitimate claim as the world's best.
"The winner on Saturday has as much credibility and as much right to be called the future of heavyweight boxing as all of the others," Bunce told the Radio Sport Breakfast.
He also believed that while the heavyweight titles continue to be split over four organisations, eventually the champions would have to come together in order to survive.
"All the guys that are involved in world title fights, because none of them are dominant, they'll all want to show they're dominant. And that means they will all eventually have to fight each.
"Those four guys [Anthony Joshua, Deontay Wilder, Tyson Fury, and potentially Joseph Parker] they need each other to become massive."