Usyk - who inflicted the second defeat of Joshua's career to become heavyweight's unified champion - has revealed he is now back in training for the delayed bout after serving time in Ukraine to defend his country from attacks by Russia.
The Ukrainian government has given Usyk the green light to begin his training camp and the former cruiserweight ruler confirmed his intentions online.
In an Instagram post, Usyk said: "I decided to start preparing for a rematch with Anthony Joshua."
K2 promoter Krassyuk has said they are now in discussions to fight in the Middle East.
"Saudi is the place we are in discussions with at the moment," Krassyuk told BBC Sport.
"Late June is the date we are looking at. Nothing has been confirmed on paper. We are working on it."
"There are other options but we take it step by step," he added.
Saudi Arabia isn't new to boxing. It held the World Boxing Super Series final between George Groves and Callum Smith in 2018 as well as Amir Khan's win over Billy Dib.
The biggest event of them all though was the rematch between Joshua and Andy Ruiz Jr. in 2019. AJ avenged his defeat to Ruiz, outpointing Mexico's first heavyweight champion to become a two-time unified champion.
Planet Sport have been informed that Joshua wants to earn £50million for the rematch should it take place in Saudi and as it stands, he is well on track to making it with Saudi placing £90million on the table to stage the fight.
June will be the date
While London also remains in the running, one thing is for certain is that it will take place in June, with Eddie Hearn repeating Krassyuk's claim.
Hearn told The DAZN Boxing Show this week: "Obviously now everybody's made their statements, Usyk's come out and said, 'I'm starting camp,' so that fight is a go for June.
"We're now going through all the various offers from different countries to stage that fight, with [Usyk's promoter] Alex Krassyuk.
"The Middle East is obviously very interested in that fight, we'd like the fight in London as well if possible.
"I think probably this week, early next week, we'll start firming up some dates. But, as I said: Usyk-AJ rematch definitely to take place in June."