The problem for Parker and promoters Duco Events is that he doesn't feature on Joshua's hit list for next year.
Joshua listed Wladimir Klitschko, former world title holder David Haye and WBC champion Deontay Wilder as the fighters on his 2017 dance card.
Three big fights in a year is considered a big challenge for any boxer, so even if Parker gets past Andy Ruiz Junior on Saturday night and lands the WBO heavyweight title, Duco may have to wait longer than anticipated to meet Joshua whom they have had in their sights for some time.
Joshua made no reference to the Kiwi boxer in the lengthy Daily Mail interview where he discussed the merits of Klitschko, Haye and Wilder.
Of the 40-year-old Klitschko who is aching to regain the heavyweight crown he lost in that upset by Tyson Fury, Joshua said: "Wladimir has been a truly great champion. But I have sparred with him and since then I have improved a lot while he is getting older. I had better fight him sooner rather than later. Before he retires."
That fight is pencilled in for Wembley Stadium or Cardiff's Millennium for April 29.
Joshua laughed at fellow Londoner Haye's threat of knocking him out in the first round:
"David keeps saying what he's going to do to me and how I will avoid him. Well, if he can get through his March fight with Tony Bellew I will be absolutely fine about fighting him."
"He's a good boxer and he's turning ours into a fight the people want. Sometimes that's how it works and I'm OK with that."
Wilder is recovering from a broken hand and talking about a title unification fight towards the end of 2017. Joshua is confident he will still be unbeaten and told the Mail: "I'll be ready and waiting. Three fights a year is not close to being too many for me."
That last quote might be the one Parker and Duco are hanging on.