Below, we take a look at the timeline of events for a summer showdown which diminishes by the day.
Joshua avoids Pulev upset
In December, AJ made a triumphant return to the ring at Wembley's SSE Arena in front of 1,000 fans.
A combination of power and patience saw Joshua prevail as he knocked the Bulgarian out in the ninth round with a flurry of uppercuts doing the damage.
"Whoever has the belts I want to compete with. If that is Tyson Fury, let it be Tyson Fury," said Joshua.
Two-fight deal agreed
After being in negotiations since December, both parties 'put pen to paper' to fight each other in March.
At the time of the news, Hearn was hoping to have everything wrapped up 'over the next few weeks'.
Fury rules out Joshua fight
A frustrated Fury backtracked on the news of a two-fight deal being agreed in March by suggesting a trilogy bout against Deontay Wilder could be next.
He told iFL: "I have two fights this year and I don't give a f*** if they are with, Joe Bloggs, Fred Flintstone, Mike Tyson, anybody. I just want to fight this year.
"Don't write Wilder out of the equation next, I could be having the trilogy fight with him yet."
What have they signed?
Despite positive news about the developments of the fight, Fury's father John Fury questioned whether the fight would happen.
Fury Snr said on BT Sport: "What have they signed? They've signed nothing in my eyes. They've got no date, no venue, no nothing.
"What does it mean if you can't get a date and a venue? What does it mean if no one is willing to put in the money?"
Dismissing Fury Snr's comments, Hearn claimed he was as 'confident' as ever of delivering the bout.
"We're in a good place. I saw John Fury's comments. It's almost like they don't really want the fight. I'd like them to talk it up rather than talk it down.
"We're quite aware that there has been a global pandemic. We're aware that it's not easy, but we're out there grafting away every day to get this done."
Promoter Bob Arum backed up Hearn. "As far as I'm concerned, I've been working on it, and all the points have been agreed.
"That's what each side has said. Now, we are scrambling around to get the thing signed and everything.
"But I can say clearly, based on my view on everything, that there are no more issues."
Big offers on the table
By April 12, the "Gypsy King" seemed more upbeat about the prospect of facing Joshua by revealing there had been some big offers on the table from various countries to host it.
"Just had some big news. Three or four big offers on the table," Fury said.
"Interest from Saudi Arabia, Qatar, Uzbekistan, Russia, America, England. Some big, big offers on the table.
"I'm going to go through them on Sunday and hopefully we get this big fight on. Let me smash this big dosser."
"Both sides have approved the site offer that they want to go with, and now we're just finalising the site deal and we're in a great place," Hearn said on April 15.
"I saw Tyson yesterday. I just messaged him and said, 'I'm in Vegas, I'm in your hotel if you fancy a cuppa'.
"We just had five or 10 minutes together and it was good, because I don't represent Tyson Fury, so I don't know what is in his mind.
"What he basically cemented in my mind was, this is the only fight he wants, and I know that's the same with AJ."
$150million is believed to have been the deal agreed for the site fee.
Fight 'as done as it can be'
"It's as done as it can be. It's non-stop at the moment, but it's happening, it's 100 per cent happening," Hearn said.
McCracken's position in doubtRob McCracken, manager and trainer of Joshua, had his position in the corner put under threat with the date of the fight potentially clashing with the Olympics in Japan's capital.
"We haven't finalised an exact date, July 24 is the rough date but it may leak into early August but no later than that. It's impossible to schedule anything without clashing with something.
"I know AJ and Rob have been talking accordingly so I am sure they will work it out.
"The date we get given is when the fight takes place and the guys know it will be around the Olympics, it could be inappropriate but it is the biggest fight in boxing and the biggest moment in AJ's career. We have to work it out."
Fight dead in the water
In a shocking outburst, Arum said the fight between Fury and Joshua had collapsed after not receiving the finer details of the site fee.
"Maybe we'll breathe some life into Wilder, and Fury will fight Wilder and Joshua will fight (WBO mandatory challenger Oleksandr) Usyk," said Arum to BoxingScene.com.
"Eddie Hearn is busy trying to sell the London Bridge," Arum continued.
"Let me tell you - last time I talked to Eddie was early last week and he said he was going to have a signed agreement from the Saudis in 24 hours.
"Well, he's a little late. Wouldn't you be pessimistic if you haven't heard from him or anybody for a week?"
Fight expected to be made official
Hearn promised an announcement on the week of May 3 after ridiculing the comments made by Arum about the site fee deal.
"Bob's ego is out of control. That sort of generation it's all about control and power for them," Hearn told BBC Sport.
"Let's all do our job. I am not looking to upset Arum, I'm just saying 'you will get the latest version of long-form and we will get it done'.
"What is Fury going to do? Fight Deontay Wilder for a fifth of the money?
"The back and forth, I suppose it just comes with the territory of the mega fight.
"To anyone listening, I really apologise for the backwards and forwards as you're probably getting bored of it.
Saudi Arabia confirmed as host
"It's a very bad secret that the fight is happening in Saudi Arabia," Hearn said. "I don't mind giving that information, Bob Arum's already done it.
"It's the same people we did the deal with for Andy Ruiz, that event was spectacular. As partners, they were fantastic as well, so we're very comfortable.
"We're very comfortable. Anthony's comfortable, he knows those people. They delivered on every one of their promises last time, we're ready to go.
"In terms of a global spectacle, it would make sense to go on the 14th," Hearn added. "That's one of the other things to tick off, hopefully, in the next few days."
Venue and date agreed
Hearn revealed plans of creating a new stadium for the event in the Middle East and promised fans it would blow their minds.
"They want to create something very, very special. Last time they built a stadium for the Andy Ruiz Jr fight in just seven weeks and it held 18,000.
"They have the opportunity to hold it indoors but they want to create something that will shock the world. They want to build a stadium just for this fight.
"August 14 will be the fight date, which is good news for Joshua with his trainer and manager Rob McCracken available.
Fury agrees Joshua fight
The "Gypsy King", heavyweight's WBC king, uploaded a video on social media and revealed he had agreed to fight Joshua.
"I have just got off the phone with Prince Khalid of Saudi Arabia and he told me this fight is 100%, August 14.
"All eyes of the world will be on the Kingdom of Saudi Arabia. I cannot wait, I repeat, cannot wait to smash Anthony Joshua on the biggest stage of all-time.
"This is going to be the biggest sporting event ever to grace the planet Earth. Do not miss it."
Arbitration hearing puts fight in doubt
Twenty-four hours on from Fury's announcement, the fight was thrown into jeopardy following an arbitrator's decision to rule in favour of a trilogy bout against Wilder before Joshua.
On May 17, Daniel Weinstein upheld Wilder's claim that he is contractually due another meeting, which must take place before September 15 this year.
The Joshua-Fury will collapse unless they can offer a substantial fee for Wilder to step aside.
Fury-Wilder 3 set for July 24
Promoter Arum claimed the Allegiant Stadium was reserved for a trilogy showdown between Fury and Wilder after refusing to pay a fee to force the American to step aside.
"We're not paying Wilder to step aside," Arum told ESPN.
"It's better to get rid of him and go about our business. We can make the Fury-Joshua fight for November or December."
Joshua-Usyk negotiations begin
Oleksandr Usyk - the WBO mandatory challenger - could replace Fury as Joshua's opponent and has started talks with Hearn.
Alexander Krassyuk - Usyk's promoter - admited he was open as to where the fight takes, including Saudi Arabia.
"Usyk is mandatory for WBO and the only obstacle that made them sanction the interim was the huge unification between Fury and Joshua.
"And if the fight is off then there is no other obstacles and Joshua has to deal with his mandatory."
If you asked me I would be happy to make the fight in Kiev. This is just my desire to make it," Krassyuk added.
"In London? Well you never know. Maybe another city in the UK or Saudi Arabia or any other spot on planet earth. We'd do it."