Meanwhile the WBC has confirmed plans to order the Gypsy King, 33, to defend his belts against interim titleholder Whyte, 32.
Arum revealed Whyte and Joe Joyce are among the frontrunners but Fury will ultimately have the deciding vote.
"Who Fury fights next will be determined by Fury," Arum told Sky Sports.
"If the fight is in the UK, I would think Whyte would be a good possibility, as well as Joyce."
The Boxing Hall of Fame promoter also teased a possible homecoming bout for the Gypsy King - but there are a few strings attached.
"Frank Warren is going to Manchester to meet Fury to work out a date. It could be March or April, but no later than April," he revealed.
"A date that would be appealing to us in the US, even if the fight took place in the UK, would be the middle of April because we have a college basketball tournament called March Madness which the country goes crazy for. It is tough to find a date for a big fight [during March Madness].
"We will figure out who and when Tyson will fight next."
Fury's co-promoter Arum is also adamant a super-fight with Oleksandr Usyk will happen at some point next year despite Joshua triggering a rematch clause in his contract.
He added: "You ask anybody in the world: 'Who is the heavyweight champion? Who is the best?'
"There would be close to unanimity in saying Fury, but that doesn't denigrate Usyk who is a friend of mine.
"He is the one guy who would be the most competitive with Fury.
"Hopefully next year that fight can happen.
"With all due respect, I don't give Joshua much of a chance in a rematch with Usyk."News Now - Sport News