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He said both parties are currently in the process of getting all the contracts signed, with a date and location to follow.
But Oleksandr Usyk may well have thrown a spanner in the works as his promoter, Alexander Krassyuk, has demanded the WBO to make the "courageous decision" to enforce his mandatory world title shot.
He wants his fighter to challenge for the WBO title, as well as the other belts - meaning a delay to Fury vs. Joshua.
Krassyuk told Sky Sports: "If AJ vs Fury is not likely to happen this year or is rescheduled until the end of the year, AJ has to make a mandatory defence against Usyk unless he relinquishes the title.
"The WBO has to gather strength and to make the courageous decision - to order AJ vs Usyk.
"Otherwise boxing will accelerate its decline in popularity due to unfair and preconceived politics."
Usyk has been linked with a fight against Joe Joyce for the interim title amid Fury vs. Joshua talks.
But Usyk vs. Joyce appears to have collapsed after failed discussions.
Krassyuk added: "Usyk cannot make any move as there's no certainty around.
"Usyk is doing well, safe and sound, fit and working hard. And is ready to face whoever the WBO legally nominates.
"But my last conversation regarding Joyce took place in the middle of January. I talked to George Warren [part of Joyce's promotional team]. Since that time, we have hardly moved anywhere."
Unbeaten Usyk (18-0) is 2-0 at heavyweight having defeated Chazz Witherspoon and Dereck Chisora.
Joyce's last fight was a stoppage victory over Daniel Dubois.
As for Joshua, he last fought in December 2020 when he took out IBF mandatory challenger Kubrat Pulev.
Fury, meanwhile, hasn't fought since destroying Deontay Wilder in February 2020.
Will Usyk agree to face Joyce, paving the way for Fury vs. Joshua for all the marbles? Stay tuned.