Joshua was hoping to unify the heavyweight division with a blockbuster clash against Deontay Wilder.
But the American is instead thrashing out terms with Tyson Fury for a rematch of their controversial showdown in Las Vegas.
The WBC belt holder is refusing to speak to Joshua’s camp until he has attempted to defend his title once again.
It means Joshua is left with a dilemma of his next opponent – and with a rematch against Dillian Whyte looking ever more unlikely – Hearn is trying to get his cash cow to box in the USA against Jarrell Miller instead.
“There was a clock ticking for Wembley. I think we can rule that out of the equation right now,” Hearn told Sky Sports News.
“April 20 looks like it could be Dillian Whyte at The O2 Arena, obviously if they don’t fight.
“It could be Dillian on April 20, Joshua in New York. Still a long way to go. Plenty of twists and turns left.
“But June 1 is some weeks away, but obviously we want to get it announced.
“AJ wants to know what he’s doing, and hopefully by end of this week, the weekend, we could be in a position to announce his next fight.”
If Joshua was to agree on terms with Miller then the pair are looking at a showdown at New York’s Madison Square Garden.
“Looking at the Miller fight,” Hearn told Sky Sports News.
“New York is something that we didn’t expect, but as we talk more about it, as we speak to great venues like Madison Square Garden, it’s starting to sound quite special.
“Not just that fight, but also creating a weekend in June for British fight fans to remember for a long time.
“We’re stacking the card with major championship fights for the young British talent, for established British talent as well.
“We’re not done with Jarrell Miller. We have deep talks progressing now.
“There is no deal yet, but right now, that looks like a strong possibility.”