Joshua's promoter Hearn said earlier this week there was "a clear desire from both sides to make the fight", and that it could be scheduled for November or December this year if a deal could be struck, Sky Sports reported.
Hearn has held meetings this week about arranging the fight and, while he would not be drawn on the outcome of the talks, he feels no more could have been done to agree a deal.
He told Sky Sports, “Well, I am not going to say much until I know for sure. I'll have a lot to say on Tuesday.
"I feel like we've done absolutely all we can. But again, I think less is more at this stage. Our job is to deliver the undisputed fight.
"It's been frustrating and I think people are beginning to see the truth. But again, I'll be quiet for now and let that truth unfold."
Before he can focus on potentially fighting WBC champion Wilder, Joshua – who holds the WBA, WBO and IBF belts – has to contend with Jarrell Miller, who he fights at Madison Square Garden on June 1.
Hearn insisted Joshua has not been distracted ahead of his fight with the unbeaten Miller, saying, "I spoke with AJ on the days of those meetings [about the potential fight with Wilder], he was just like 'let me know'. He doesn't want to bring himself into that line of thinking before June 1.
"This is heavyweight boxing. You've got Jarrell Miller down there in Miami, I am watching him in camp, he's training like a man possessed because it's his chance to become world heavyweight champion.
"So if you start thinking about Wilder in November or December, you could end up looking very, very silly. From AJ's point of view, it's Jarrell Miller."
While a unification fight between Joshua and Wilder would undoubtedly be one of the biggest the sport has seen in recent times, a deal has been difficult to make.
Wilder instead fought Tyson Fury last December, although terms for a rematch following their draw were not agreed, and he has now been ordered to defend his title against Dominic Breazeale.