WBC champion Wilder is yet to agree to a unification fight with Joshua, who is aiming to hold all four of the major heavyweight belts.
The lengthy negotiations have once again stalled after delays in the American's camp returning the contract they were sent by Hearn.
Now, the World Boxing Association (WBA) has ordered the Briton to sign for a mandatory title defence against Povetkin within 24 hours, and Hearn believes the governing body has run out of patience.
Hearn said to Sky Sports: "I think they [the WBA] have just said enough is enough. They have been waiting and to be fair to them, they have been patient, but [WBA president] Gilberto Mendoza has clearly decided enough is enough and we've got to move.
"We need to know what you're doing, you're mandated to fight Alexander Povetkin, and I think Povetkin's people are getting extremely restless as well.
"I think Anthony is frustrated... he feels people feel he might not want this fight. He wants that fight more than anything.
"Deontay Wilder is another fight that [Joshua] wants badly. We can't do a lot more than we're doing. We sent the contract nearly nine days ago now.
"We're not even necessarily expecting a signed contract back. We just want your comments. If my fighter wanted a fight, and we received a contract, I would be back with the comments within 24 hours.
"They know we're under pressure from the WBA and it all feels like a big game. It's very, very frustrating and right now it looks like Povetkin is next."
— Anthony Joshua (@anthonyfjoshua) June 12, 2018
Despite the problems that have come with sorting out the showdown with Wilder, Hearn says Joshua's main focus is unifying the division.
He added: "The important thing for us is to maintain the belts and not be disrupted by people playing games or people who want to mess us about, because we're not going to allow that to happen to Anthony Joshua's career.
"If it is Alexander Povetkin, it will be in September, that's for sure, and then we fight Wilder straight after, if he signs a contract.
"But the way they are going at the moment, I can't tell you whether this contract gets signed in 10 days or 10 years."