Representatives of the two Britons are in dialogue with venues keen to stage the fight in a bid to make clear how much money the contest could generate.
Neither side is negotiating monetary splits or wider demands at this stage.
But Joshua’s promoter Eddie Hearn said they are “talking” about how a bout for all the heavyweight belts could happen.
One source close to the discussions told BBC Sport they now believe the fight “will happen” and confirmed talks were under way.
Authorities in Saudi Arabia – the country that staged Joshua’s rematch victory over Andy Ruiz Jr in December – are keen to secure the bout.
After working closely with Hearn to host Joshua-Ruiz, a member of the country’s royal family sat next to promoter Frank Warren in Las Vegas to watch Fury win the WBC belt from Deontay Wilder in February.
Wilder has a contract to face Fury again, while Joshua – holder of the IBF, WBA and WBO belts – is slated to face Bulgaria’s Kubrat Pulev when sport resumes after the coronavirus shutdown.
At this stage, establishing how much money could be generated by a Joshua-Fury bout is seen as key as it would allow clarity on what could be offered to Wilder and Pulev in order for them to break the contracts they have in place.
The ‘step aside’ money on offer for both men would be several million dollars and there is a feeling privately that Wilder – who has just had surgery – would take it, even though those closest to him have refused to acknowledge the prospect.
Wilder was due to face Fury for a third time but both dates in July and October have been wiped out by the coronavirus outbreak. It is not known as to whether the contract in place for the fight could lapse as a result of the delays but if it did, it would free Fury to pursue his fight of choice.
“Negotiations aren’t under way,” Joshua’s promoter Hearn told Sky Sports on Thursday. “What I can tell you is we are talking. We are all on the same page. You will get this fight, it’s just a case of where and when.
“There is the major hurdle that we are both under contract for other fights. Everything is solvable with money.”
Delivering the fight – which would create the first heavyweight in history to hold all four belts – faces further hurdles even if Wilder and Pulev step away from their respective bouts.
Promoters Hearn and Warren would need to briefly overcome their rivalry, Fury’s promoter in the US Bob Arum would need to be on board, financial splits would need agreeing and rival television broadcasters would need to work as one.
A source close to the talks stressed the need for everyone involved to work in harmony, a feat that has at times been hard to achieve in securing the biggest bouts in the sport.
On his podcast, former world super-middleweight champion Carl Froch assured listeners that regardless of politics, bouts at the highest level will happen if the fighters want them.
“Trust me, the fighter at the top level is the boss,” said Froch. “It’s the fighters that aren’t making the fight happen. If two fighters actually want the fight, have a 50-50 split, remember that the fight doesn’t happen without both of you, so then the fight happens.”
While talks are at a very early stage, any bout would be aimed at late in 2020 or early in 2021 and in the interim, all parties will learn if it would be possible for fans to attend any fight given the current ban on mass gatherings in most countries.
And the sums that could be earned from the contest after a boxing shutdown that has presented financial challenges for promoters and broadcasters would undoubtedly be welcomed.