Joseph Parker would welcome a fight with Tyson Fury in 2019 if the lineal heavyweight champion is unable to agree a rematch with Deontay Wilder.
Fury returned to the top echelons of boxing last year in his first fight with Wilder, the WBC title bout judged a split-decision draw in Los Angeles.
A second meeting between the pair was ordered by the governing body, yet an official announcement has yet to be made.
Should they not be able to finalise a deal to face each other again next, David Higgins - Parker's promoter - has confirmed the New Zealander is keen to face the Brit.
Speaking to Sky Sports News, Higgins said: "When people talk about Joseph Parker fighting Tyson Fury, obviously there's going to be public interest, because of the family connection with Joseph's victory over Hughie Fury [Tyson's cousin].
"It's currently Parker one, Fury nil.
"If the terms were right, we'll go maybe to America or even to England to fight Tyson Fury.
"We won't chase after them, they hold the cards with Tyson Fury, but if they're serious, they are welcome to communicate and we would look at that opportunity too."
After successive losses to Anthony Joshua and Dillian Whyte on British soil, Parker was offered the chance to take on Dereck Chisora on April 20 but declined the opportunity due to a lack of preparation time.
Higgins, however, confirmed they would be willing to reschedule, should Chisora and his team still be interested.
"I saw comments by Dereck Chisora's manager or promoter David Haye basically saying that our reasons for pulling the pin are trivial," Higgins added.
"That totally undermines the historical reality. We ran a short camp for Whyte, and we weren't quite happy with the length, and we learned from that.
"Joseph Parker has shown he is willing to fight anyone, anywhere, any time on the right deal, but the terms have to be fair. No, Haye disregards those facts.
"I think they thought they could get an unfair advantage again by leaving Joe with a jet-lagged, short camp. That's not going to happen under my watch. The message to British boxing is this - fight fair.
"Dereck Chisora should give Joseph a fair and decent camp. We'll fight Chisora anywhere, any time, but we want at least a nine or 10-week camp, and fair terms."