The former heavyweight champion was expected to take on Oleksandr Usyk before he returned to Ukraine to protect his country from Russia's invasion.
It is increasingly unlikely Usyk will not fight this summer and he could be out of the ring for the rest of 2022.
Joshua is now assessing other options and former amateur opponents Joe Joyce and Otto Wallin are among the names in the hat to face him.
AJ - who surrendered the WBA, IBF and WBO titles to Usyk - has reportedly appointed Angel Fernandez as his new head coach after parting ways with Rob McCracken.
Fernandez has worked with Joshua since his rematch victory over Andy Ruiz Jr in 2019 and will now lead him in his bid to become a three-time heavyweight champion.
In a tweet, Joshua said: "Announcement soon come."
Promoter Eddie Hearn gave an update on Joshua and revealed an American former heavyweight world champion was on his radar.
"AJ talked about Deontay Wilder. If you said to AJ right now, who do you want to go for, I think he would say Wilder," Hearn told iFLTV.
"It's a big fight. It's not an interim fight is it. Let's be honest, it could be a bigger fight than Usyk. He has no fear of fighting anyone.
"He is all about legacy, resume, challenges. He's calling out the top five, the top 10. He has given me a wish list he would like me to enquire about.
"He [Joshua] is being quite vocal at the moment. He is on it. I sat down with him last night and he wants to fight.
"He is raring to go and he feels great. I believe, he believes and the team believes he is going to come back and prove he is the best heavyweight in the world.
"There are obviously conversations going on with Usyk but the one thing that baffles me when people talk about Anthony Joshua is that this young man has boxed everyone and he will box anyone.
"He fought Usyk when people said you should just swerve that because he is a really tough mandatory. No, he boxed him and now he wants to go straight back into a re-match.
"He turned down £15million to even go in with him. So, AJ will fight absolutely anyone. He's come to me and said find out what is going on with Usyk.
"But, if I have to have an interim fight here are some of the names I like. He's told me to make them so offers so we can progress. One thing is for sure, he will be fighting a top 10 heavyweight.