Hearn had told the Herald a fortnight ago that he was hopeful a press conference could be held this week announcing the fight in which Parker's WBO heavyweight world title and Joshua's IBF and WBA "super" belts would be at stake, but a public meeting between the pair isn't likely to happen until next week.
"The public might wonder why it's taking so long, but boxing is unique in that there are usually no long-standing agreements over things like TV rights like in other sports… this fight could have a turnover of more than $NZ40million so you have to get it right," Higgins added.
Parker, who turned 26 yesterday, is back from a holiday in Samoa and is prepared for an imminent trip to London, Higgins said, adding that he had discussed what could be a lively press conference with Hearn.
Read more: Parker vs Joshua likely to be announced this week
"Eddie and I have talked about it. Traditionally they have been humble and respectful in the build-ups to their fights but that's not the case this time… with talk about Joshua's chin and how he's been rattled mentally."
The fight date and venue has yet to be confirmed but it's almost certain to be at Cardiff's Principality Stadium in late March or early April.
Higgins said of the Principality, formerly known as the Millennium Stadium: "It's a good option. It holds 80,000 people which is nearly twice the capacity of Eden Park. It would make for a huge event.
"If we get there we will be asking New Zealanders and Samoans to get patriotic. People will have their own views about how the fight will go but we will be the underdog against a very well-funded and well-hyped opponent from England, whereas we're running on the smell of an oily rag in New Zealand."
Higgins said he had already received inquiries from travel agents regarding supporters' tours. One surprising element to Parker's last fight – against Hughie Fury in Manchester in September – was how many New Zealanders were in the crowd, and there are likely to be many more in Cardiff should the fight be held there.
"There could be thousands there. And if it is held in Wales, we know how the Welsh view the English - perhaps they could be cheering for Joe too."