Joshua's promoter, Eddie Hearn, has proposed a 70-30 split with Parker, whose team is countering for 65-35.
"It seems to me with a little tugging and so forth, they can do 2/3 and 1/3 and that's what I think is going to happen," Arum said.
Negotiations for the blockbuster fight have been ongoing for weeks, with Parker's camp launching an aggressive public campaign to lure Joshua into the ring.
During a news conference last month, Parker offered money for footage of the Briton being knocked down during sparring.
Parker also questioned Joshua's motives this week, with the Briton's promoter, Eddie Hearn, reluctant to meet the WBO champion's asking price of a 35 per cent purse share.
Joshua, 28, told the BBC the 25-year-old was "trying to mislead the public's opinion".
"I think it's not nice, I don't really respect it and I have no time for it," said the IBF and WBA champion. "What's he trying? Be the big bully? Demonise everything I have done?
"In Formula One, golf, tennis, rugby, they are very classy people, respectable about their peers. Then you have people like Joseph Parker holding a press conference talking about everything he thinks I am."
Should the fight happen, the winner could then face WBC title holder Deontay Wilder in a bout which could unify all four major titles in the heavyweight division.