The Ukrainian claimed the IBF, WBA and WBO belts with a unanimous decision victory over Joshua at the Tottenham Hotspur Stadium last month.
Two weeks later Fury defended his WBC crown with an 11th round knockout of Deontay Wilder in Las Vegas.
Many are now calling for Usyk and Fury to meet for all the belts, but Joshua has already triggered the rematch clause to face the former undisputed cruiserweight champion for a second time.
Usyk’s contractual obligation means he is forced to wait for a Fury fight, but his team insist he wants that challenge providing he comes through against Joshua again.
Speaking to Sky Sports, his promoter Alexander Krassyuk said: “[The Fury fight] will be after Usyk defeats AJ in the rematch.”
Krassyuk also revealed how Usyk reacted to the heavyweight classic between Fury and Wilder, which put an end to their three-fight rivalry.
When asked if Usyk was impressed by Fury-Wilder III, Krassyuk said: “He was. And he was impressed with how the boxers fought without showing boxing skills. They were trying to [badly hurt] each other.”
Usyk and Fury are now the only two at the top of the heavyweight division who are undefeated as professionals.
While the Ukrainian rematches Joshua in the early part of next year, Fury looks set to defend his belt against Dillian Whyte – that is, providing Whyte beats Otto Wallin at the end of October.