The Ring Magazine's Mike Coppinger was first to report the story.
Hearn went on to state that the idea behind Joshua's fight with Miller is to boost his profile in the United States.
And Hearn is hopeful an announcement will be made soon.
Joshua, undefeated after 22 fights, with twenty-one knockouts, faces 30-year-old Miller, who has also competed at the highest level as a kick-boxer, and is unbeaten himself in 24 boxing contests, with twenty KOs.More news: VP Mohadi Now President As Mnangagwa In Ethiopia For AU Summit
Joshua, the 2012 Olympic super heavyweight gold medalist, is a man who needs no introduction.
Team Joshua then turned their attention to a rematch with Dillian Whyte, but "The Body Snatcher" rejected the initial offer proposed to him.
But Hearn had issues closing a deal with Whyte, and Joshua also came around to the idea of boxing in the United States.
Russian powerhouse Alexander Povetkin - vanquished by Joshua in September of past year - looks the likely favourite, whilst American Dominic Breazeale - also defeated by Joshua in June of 2016 - has also been linked. 'April 20 looks like it could be Dillian Whyte at The O2 Arena, obviously if they don't fight, ' said Hearn. However, both sides could not agree on the financial terms.More news: Vet sentenced for implanting heroin in puppies as drug mules
Anthony Joshua has moved one step closer to fighting Jarrell Miller after his promoter, Eddie Hearn, revealed that a deal has nearly been finalised.
But a rematch has fallen through, with Joshua's promoter Hearn revealing why. After that, it was rumored in boxing circles that Joshua could eventually make his USA debut.
Many boxing fans would have loved AJ to fight Deontay Wilder in a unification match, but that was unlikely after the WBC called for a rematch between the Bronze Bomber and Tyson Fury following their controversial draw on 1st December.
Alexander Povetkin has "always" been interested in Dillian Whyte after being named on a shortlist for the British heavyweight's next fight.More news: Ceferin re-elected unopposed as UEFA President