According to Declan Taylor of Boxing News, Hearn said he expects the two sides to agree upon and finalize a venue for their fight in the coming days.
Fury and Joshua signed on for the fight last month, giving them 28 days to finalize everything. Hearn said that while the sides could agree to an extension, the goal is to get everything done within the 28-day timetable, and he believes they will:
"We always had a timeframe in place in the agreement that everybody signed. That can be extended, but it's not the intention to extend it, and we are all working to that timeframe. Really, I think end of next week it will be done.
"They are going to be presented with a few proposals on where to do the fight and everyone has to agree on where to do it. There is no other fight out there that comes close for either guy. July is the date. We can't wait. [Joshua] has started his training camp and Fury has been training very hard. They all want the fight."
It is unclear where the fight may happen at this juncture, but Hearn is fresh off a tour across multiple continents during which he held six different meetings about potential venues.
Taylor noted that Saudi Arabia has looked like the favorite to host the fight, with Qatar, Dubai and the United States also in the running.
If the fight gets finalized, it will set in stone one of the most highly anticipated heavyweight clashes in recent memory.
The 32-year-old Fury is 30-0-1 in his career, and he made up for the draw with Deontay Wilder in his most recent fight, decimating Wilder by seventh-round technical knockout in February 2020 to win the vacant WBC and The Ring heavyweight championships.
Fury's British countryman, Joshua, is 31 years old and owns a career record of 24-1 with 22 wins by way of knockout.
The lone blemish on Joshua's record is a stunning TKO loss to American Andy Ruiz in June 2019, but Joshua bounced back to beat Ruiz later that year, and he then defeated Kubrat Pulev by knockout in December 2020.
Joshua is the reigning and defending WBA (Super), IBF, WBO and IBO heavyweight champ, meaning a fight with Fury will result in the crowning of one undisputed heavyweight champion.