With Fury set to return to action for the first time since ending Wladimir Klitschko's heavyweight dominance in November 2015, many are billing the prospective meeting with current WBA Super and IBF world champion Joshua as a simple match-up of boxer vs. puncher.
According to reports, the contest will take place on 31 March, at Cardiff's Principality Stadium.
Higgins also revealed that Parker remains in New Zealand while he tries to finalise a deal for the two to meet in the ring.
"I was bantering with David Higgins yesterday".
The two men are now expected to come face to face next week, with Joshua's promoter Eddie Hearn this week promising fireworks after Parker and Higgins aimed a string of critical comments at Joshua.
"The possibility of this fight happening, I've visualised happening - fighting Anthony Joshua and knocking him out - and that's what I'm going to do".
GETTY IMAGES British boxing star Anthony Joshua hasn't been happy with the taunts coming from Joseph Parker
"Some people only talk but talk's cheap so you're stepping up trying to unify and we think with your style and Parker's, it will be good for the fans and it will be the fight of the year".
"We're excited about Joshua", Higgins told Behind the Gloves.
"Tyson Fury has too much skill and too much altogether for Anthony Joshua".
"We need these belts, there is no secret, and they know that as well", he said.
Talks have been quite amicable, meaning Parker was happy enough to make the long trip to the United Kingdom to take part in a press conference to confirm the fight early next week. We are very close.