The Briton holds two of the world heavyweight crowns, while Parker is the WBO champion, and both fighters are yet to taste defeat.
But the chances of a 2018 bout seem slim after the first round of negotiations.
Duco director David Higgins last week said Parker wanted a 40-60 split from the fight earnings however he has told Sky Sports that the first offer from Joshua's manager Eddie Hearn was ' ridiculously low'.
"I got this weird email from Eddie's email address, but he must have been hacked," Higgins told the British network.
"He made the most ridiculously low offer. It could have been the most insulting offer in boxing history.
"To expect 40% is actually quite reasonable, because you have earned it, and it's a unification.
"Of course I have mentioned it [to Joseph Parker] and he just laughed like I did.
"I'm not going to reply, because I don't think it was Eddie Hearn. I reckon someone hacked his account, it was a scam. I reckon Eddie respects boxing and I reckon Anthony Joshua wouldn't want to insult Joseph Parker.
"Joseph has worked his way from the ground up and earned the right. Joshua, I think, would understand and respect that, so it can't possibly be AJ or Eddie that made the offer. It must be an email hack."
Higgins said Parker was happy to wait and fight WBC champion Deontay Wilder after the American and Joshua had faced off.
"I'll give you a simple answer. They pay us 40% and not a cent less, or they will fight Wilder, who will obviously win and then we'll fight Wilder 50-50," Higgins told Sky Sports.
"If they want to go fight Wilder, they can, and then we'll fight Wilder on a 50-50 basis later in the year, once he has all three belts.
"We will come to England and fight AJ, but 40% is the bottom line and I can give my word now, not 1% less."
Last week the Parker made it clear that he wanted a shot at the Brit.
"I want to fight Joshua," the 25-year-old Aucklander said on Wednesday.
"He's got two belts, I have one belt. I want to test his chin and put on a great show. I would like to fight him next."
Higgins said he began exchanging emails with Hearn in the past week or so.
"We both connected again yesterday and my message was Parker would fight Joshua next and Hearn's message was Anthony Joshua would fight Parker next," he said.
"So it's really down to a question of the deal and money."
Higgins said any agreement had be a fair one and be respectful of Parker having earned a world title.
He said there's no cut-off date for the negotiations.
"It's a moving feast," he said.
"We will do a deal when it's the right deal."
Parker's last fight was in September, when he defended his world title by beating British opponent Hughie Fury by majority decision in Manchester to take his record to 24-0. He won't fight again until the new year.
If the Joshua fight fails to eventuate, unbeaten Australian Lucas Browne looks the likely alternative.
Higgins said talks had been in progress for several weeks with Browne's promoter and terms were largely agreed in principle.
"We could look at pushing the go button on that fight if we decided it was the right option."
Other possible opponents for Parker were American Bryant Jennings in Las Vegas in March and China's Zhang Zhilei in China in the second quarter of the year.
