Parker's promoter Dean Lonergan is increasingly sure that the 24-year-old South Aucklander will be given his chance against Joshua sooner rather than later after negotiations by Joshua's camp with Kubrat Pulev and Hughie Fury, cousin of Tyson, failed.
"We've made a decision as a team that anything that comes through from here on in, [trainer] Kevin [Barry] and myself will filter out first and then we'll make a decision on whether we'll take it any further because the most important thing is that Joseph Parker fights Alexander Dimitrenko and wins, that's an absolute must."
Parker fights 2.01m Russian Dimitrenko in Manukau next Saturday and a defeat would be a huge setback to his career. Joshua's promoter Eddie Hearn is set to announce his opponent this week.
"He doesn't need to get distracted," Lonergan said. "Kevin will be the ultimate arbiter of this, and Joe I guess, if they want to talk about it or not, but the closer we get to the fight, the less we'll want to talk about it."
Lonergan added: "Given that we are only two months away I would fully expect Joseph to get the call-up [to the main event] because I very much doubt that they can get a Klitschko fight over the line.
"Even if they do, Joseph will be fighting David Price on the undercard and what a great way to prepare to take on either one of those two. It's fair to say that either way you look at it, Joseph Parker is in a magnificent position to further progress his career."
Lonergan was sad to hear of Fury's struggles which were revealed in more detail yesterday by Peter Fury, the Englishman's uncle and trainer, who said the heavyweight was at an "all-time low", and at times found it difficult to get out of bed in the morning.
It is the second time he has pulled out of the Klitschko re-match, and after the likely stripping of his WBO and WBA titles it's possible his career is over.
Peter Fury said: "He is at breaking point, he is seeking help ... Nothing means anything [to him]. He's at an all-time low."
Lonergan said of 28-year-old Fury: "It's a shame that he's going through this."