Anthony Joshua remains New Zealand heavyweight boxer Joseph Parker's preferred next opponent as his team work on his schedule for 2018.

The Briton holds two of the world heavyweight crowns, while Parker is the WBO champion, and both fighters are yet to taste defeat.

"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."

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The rival promoters, Duco director David Higgins for Parker and Eddie Hearn for Joshua, have been in contact, with Higgins saying they began exchanging emails 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.