Parker defends his WBO World Heavyweight title against Fury in Manchester on September 23, with the winner placing themselves in prime position for a showdown with WBA and IBF champion Joshua.
Joshua has a rematch against Wladimir Klitschko and a challenge from IBF mandatory challenger Kubrat Pulev to get through first, but the promoters of both Joshua and Parker met on Tuesday (NZ time) to talk up a showdown between their two prize fighters in 2018.
Joseph Parker's team met Anthony Joshua promotor Eddie Hearn to discuss a potential fight next year.
Joshua's promoter, Eddie Hearn, said there was a long way to go before they would meet.
"From an Anthony Joshua promoter's point of view, we've got the Wladimir Klitschko fight, we've also got a mandatory with Pulev but we want Parker [in the English] spring/summer of next year. We want to try and add another belt to the bow."
Hearn was backing Parker to get past Fury, with fellow British boxers Tony Bellew and Dillian Whyte the obvious choices for Parker's next defence if the Manchester fight went his way.
"It's a fight, I think if it happens, they should win and then I would stay here [in the UK] to be honest with you.
"I would try and knock off all the guys that would make my profile so significant that the Anthony Joshua fight becomes a huge UK and worldwide event.
"Certainly victories over Hughie Fury and Tony Bellew or Dillian Whyte would put Joseph in a brilliant position to earn a lot, a lot of money in the Anthony Joshua fight and put him in a position where that fight is a necessity rather than a potential fight."
Photo: Getty Images (Anthony Joshua puts Wladimir Klitschko on the canvas).