Anthony Joshua lost his WBA, IBF and WBO heavyweight belts to Usyk back in September, with a rematch expected in early 2022.
However, Oleksandr Usyk joined compatriots Vasiliy Lomachenko and the Klitschko brothers in heading to Ukraine to defend their home country during the ongoing Russian invasion.
With Usyk currently enlisted with the military, a rematch is now up in the air, with doubts arising regarding whether or not the 35-year-old will fight this summer.
Meanwhile, Joshua is keen to return to the ring, and ideally wants an opponent sorted by the end of the week.
Promoter Eddie Hearn stated that this week is the "deadline" for an opponent to be decided.
"I felt Usyk would be taking the fight in June, but obviously, with Lomachenko's announcement last night, it makes you think, can Usyk come out and say, 'Nice, but I'm fighting'? So we are just saying to him we need to know.
"If you want to fight, let us know and, if not, we'll give you time, but we will fight in June. That is what hopefully we can decide this week.
"This week is the deadline really because we want to move forward. AJ is not getting restless, but he wants to fight and wants to be active."
Joshua and Hearn were seen together at the O2 Arena on Saturday night for UFC London, and shortly after Hearn said he could tell that AJ "wants to fight".
The former heavyweight champion has only been in action twice since the Covid-19 pandemic, stopping Kubrat Pulev in the seventh round at the end of 2020 before being stunned by Usyk at the Tottenham Hotspur Stadium in September.
"AJ is good and loved the UFC, but you can tell he wants to fight," Hearn said.
"He wanted to get in there and fight. He is excited, he wants to be active and that is the one thing that has been missing a lot from his career.
"I think because of his commercial obligations, but also as well as that trying to keep more active with the pandemic, it has really been two fights in two years so he feels he wants to get active again."
Should Usyk turn down the rematch, Londoner Joe Joyce has been mentioned among the possible replacements, with the 36-year-old calling out Joshua on social media.
But while that fight remains a possibility, Hearn would much rather see his fighter prepare for the eventual Usyk bout by facing a southpaw.
"It would make sense to fight a southpaw if you are preparing for Usyk, so Luis Ortiz or Otto Wallin.
"Joe Joyce is calling him out. Look, he is happy to fight anyone. He has boxed virtually everyone in the division anyway so he doesn't have a problem. We will see if the interim fight is an option.
"If it is an interim, probably London, but if not, it could be…international as well."