0448 GMT September 23, 2021
The pair is set to contest all four world heavyweight titles in a highly-anticipated bout this summer, BBC Sport reported.
Hearn said August 14 is a date both sides have agreed to and that while the fight is not officially confirmed, only administrative tasks remain.
"The Saudi plan is to allow international travelers," said Hearn.
Speaking to BBC Sport, Hearn added, "Pandemic permitting, I'd like to think by August you'd have the ability to travel to Saudi for this fight. They may have precautions in place, whether that's vaccine related or testing – I'm sure all countries will adopt different policies worldwide. But their aim is to attract overseas travelers."
Hearn said Saudi organizers are eyeing capital city Riyadh or Jeddah to play host and that they intend to build an outdoor arena – as they did for Joshua's rematch win over Andy Ruiz Jr. in December 2019.
The team behind the event in Saudi has reportedly put forward $150 million (£107m) for the right to play host. The fighters will then split more when pay-per-view revenues are added in.
"They want to build a stadium," said Hearn. "It's 24 degrees at 11:00 p.m. at night in August, which is not horrendous. They want to make it a spectacle."
Joshua will risk his WBO, WBA and IBF world heavyweight titles and has lost once in 25 fights while Fury will put his WBC belt on the line and is undefeated in 31 outings.
No heavyweight in history has held all four recognized world titles before.