Joshua beat Wladimir Klitschko after an 11th-round stoppage - the 19th knockout of his professional career - in front of 90,000 supporters at Wembley Stadium on Saturday to secure three of the four titles previously held by Fury.
Hearn said: "In terms of worldwide stardom, I said: "you win this fight and you become the biggest star in British sport and the biggest star in world boxing". Ali was one of AJ's inspirations.
Hearn, a lifelong boxing fan, said last weekend's bout was one of the best he could recall and was fit to be ranked alongside the classic 1970s trio of heavyweight fights between Muhammad Ali and Joe Frazier.
He called him out in the aftermath of the fight on Saturday, asking: "Fury where you at, baby?" It's not been discussed though.
"To me, Klitschko let him off the hook". "I don't think those were media-trained soundbites".
Ahead of his flight with Klitschko at Wembley Stadium, the WBA confirmed that Joshua could be granted a "special permit" not to fight the mandatory challenger if there was a "very serious" alternative.
While Joshua and Ukrainian veteran Klitschko retained a respectful tone towards one another both before and after their epic fight, the same can not be said of Joshua's relationship with Fury which has been marked by a series of back-and-forth taunts.
Fury subsequently had his license temporarily revoked by the British Boxing Board of Control.
Joshua said his victory over Klitschko, in which he overcame a sixth-round knockdown, showed he "can knock anyone out". Conversely, Fury upset enormous odds in Germany to shut down and befuddle Klitschko, winning a unanimous decision.
It proved to be a springboard for Joshua when he came out for round 10 and then ultimately in round 11 - when he stopped Klitschko. "I thought, "this is it, he's not coming back".
"I have been out of the ring as long as Klitschko but the difference is, I am not 41, I am 28". He showed he can recover from taking big shots.
When probed on what weaknesses he saw in Joshua against Klitschko - that Tyson or his cousin Hughie could capitalize on - Peter kept his cards close to his chest.
"I've got nothing but love and respect for anyone who steps inside the ring".