The British rivals want to fight for all the world heavyweight belts next year, provided that they overcome current challenges inside and outside the ring.
Joshua defends his WBA, IBF and WBO belts against Kubrat Pulev on December 12, live on Sky Sports Box Office, while Fury has entered a mediation process over a disputed third fight with Deontay Wilder.
But WBC president Sulaiman has given his backing for Fury to face Joshua, telling Sky Sports: “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.”
Dillian Whyte’s status as the WBC mandatory challenger was ended by a knockout loss to Alexander Povetkin, with a rematch set to be rescheduled in January, and an official ruling is yet to be made by the WBC on whether the winner will line up a title shot.