The British rivals will try to fix a unification bout next year, provided that they overcome current challenges inside and outside the ring.
Joshua will defend his belts against Kubrat Pulev on 12 December 2020, while Fury continues to ponder over a disputed third fight with Deontay Wilder.
But WBC president, Sulaiman, has given his backing for Fury’s intentions to face Joshua, saying: “There’s absolutely great hope from the world to see that undisputed fight. Tyson Fury is our champion, our pride. Anthony Joshua holds the other belts and he has been a tremendous asset to the sport. A gentleman, a great career.
“To see this showdown, Fury-Joshua, would be tremendous for everyone in the sport of boxing. We will absolutely support it.
“The WBC has no blocks right now. There is no mandatory contender. There is an issue that we are aware that Tyson Fury and Deontay Wilder have some sort of mediation process going on and that’s the only thing, but we don’t have any details.
“We’re just hoping that everything gets resolved and everybody is happy and we see great fights inside the ring.”
Another British fighter Dillian Whyte’s status as the mandatory challenger for the WBC belt was ended after he suffered a knockout loss to Alexander Povetkin, with a rematch set to be rescheduled in January. An official ruling is yet to be made by the WBC on whether the winner will line up a title shot.
Fury’s expected homecoming clash against Agit Kabayel in December has also been called off amid the ongoing dispute with Wilder.
Fury’s list of opponents is laughable in comparison to Joshua, says promoter Eddie Hearn.
Hearn insists he remains motivated to arrange a blockbuster showdown with Fury if his fighter makes a successful title defence against Pulev.
“Listen, it’s completely over to them,” said Hearn. “We have the dynamics of the deal in place. I don’t want to hear [from] Fury: ‘No, I’m thinking about fighting in March or April’.”
“Why? Just go straight into the AJ fight. It’s going to be the same timeframe. [Fury] boxed in February. It’s not like he’s been out and he didn’t box in 2020.”
“Listen, Fury doesn’t want to take a small fight. They couldn’t even get the money together to give him a fight in December, so let’s give him plenty of money. Let’s give him the biggest fight.”
Sulaiman has also suggested that Wilder will remain in well-sorted after for a possible world title shot, despite his stoppage loss to Fury in February.
“Wilder is a tremendous, important element,” Sulaiman said. “He was five years champion of the WBC. Extremely loyal. The greatest knockout ratio. The percentage is unbelievable and he is a very dear fighter, a champion in the WBC and he deserves, of course, another opportunity.
“He gave Tyson Fury the opportunity and Tyson Fury beat him, knocked him out, and of course Wilder is in the mix. He deserves an opportunity. We will see how things evolve in the coming year.”