"If we are required to fight Hughie Fury, then that simplifies things a bit," Duco Events' director David Higgins told Sky Sports.
"We are clarifying that at the moment. If the opponent is required to be Hughie Fury then we'll assess the pros and cons of holding it in England versus holding it in New Zealand, and we wouldn't rule out either.
"We would consider all options. The other thing is to reach out to Al Haymon's people about Deontay Wilder, potentially seeking to unify all of the belts.
"My understanding is that if we go to unify, it potentially overrides the mandatory, so that means we have options. We are not scared of anyone, we're not going to look to pad or dodge - we want to unify."
Anthony Joshua was expected to defend his belt against Parker, but the IBF mandatory challenger turned his attention to the WBO title after the British heavyweight entered talks over a future fight with Wladimir Klitschko.
Joshua swept aside Eric Molina in three rounds to set up a Wembley fight with Klitschko on April 29 and Higgins believes a Parker-Wilder fight would be a welcome addition to the undercard.
"Whether Eddie Hearn is willing to have two heavyweight title fights on the one card, we don't know," said Higgins.
"We could have Wilder-Parker and Joshua-Klitschko on the same card and then the winner of each fight could fight off against each other.
"I guess the other wild card option is if Tyson Fury sorts himself out and wants a shot back at his belt, because I think the WBO said once he is fit again, he could ask for a shot back. Once again that is something we would look at."