Joshua's representative Hearn has been in talks with Wilder's team over a blockbuster showdown for a number of weeks but as it stands, there remains a stalemate over where the bout will take place.
Povetkin is currently the mandatory challenger for the WBA belt - held by Joshua - and with a limited time to deal with that obligation, Hearn has suggested that the Russian could be Joshua's next opponent.
Hearn told Sky Sports News: "I don't like making deadlines because sometimes it gets people's backs up but at some stage soon we have to make a decision. We are close to closing a deal with Povetkin with [Andrey] Robinsky and World of Boxing and once the deal is closed, there is no Deontay Wilder.
"Wilder has had the latest offer from us for the last two weeks which was our improved offer and we are still talking to them and in fact, my dad is out in New York at the moment, and he might meet Shelly [Finkel] today.
"They have our offer so they have to accept it or move on. It's not a case of if you don't accept this offer the fight is dead, we will just fight Povetkin and carry on our negotiations to the next one."
If Joshua is to face Povetkin, that bout will likely take place in London or Cardiff.