The Watford-born boxer's name was sent into the stratosphere on Saturday night (29 April) after his extraordinary knockout victory against Wladimir Klitschko at Wembley, and he has now set his sights on a bout with the Gypsy King, who has also defeated the Ukrainian.
Joshua, who now boasts a flawless 19-0 record, says he will cherish the win over Klitschko but insists it still doesn't top winning gold in London.
"What can I say?" He's now 19-0 with all 19 victories by stoppage.
As boxing states, you leave your ego at the door and you respect your opponent.
If Wladimir Klitschko was to retire then a boxing era would have ended.
The Briton has retained the IBF's version of the heavyweight title while adding the vacant WBA strap. Klitschko's record now stands at 64 wins to five losses.
"The best man won tonight", Klitschko said, "and it was an awesome night for boxing".
He may not be the fighter he was at his exceptional peak, and he will decline further as a effect of such a bruising fight, but - beyond Joshua and Tyson Fury - it would be hard to argue against him beating any of the world's other leading heavyweights.
"Well done Anthony Joshua". Its really sad I didnt make it tonight..
Just five years removed from winning an Olympic gold medal in London, Joshua stopped a fighter who dominated the heavyweight division for almost a decade.
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"We are desperate for that fight because AJ thinks he wins comfortably, it is a great fight and it is the biggest fight out there", Hearn told talkSPORT.
The 28-year-old is around seven stone too heavy to fight and could be lacking a competitive edge should he face Joshua straight away.
He and Klitschko traded knock-downs in the fifth and sixth round, with Joshua appearing exhausted and just a few punches from defeat. Klitschko seized his moment and began to land flush as he took control. He became a boxer in 2007 at the age of 18.
Klitschko got up but was on unsteady legs and began swinging wildly.
But the veteran two-time champion fought back strongly to leave Joshua in trouble at the bell and a clinical right to the temple dropped Joshua in six to audible gasps.
He was up at eight and immediately had to duck a big left from Klitschko before surviving the round.
Big mistake. Joshua was given a breather and when he clawed his way back in the later stages, finding a "second wind", his wicked body shots began to sap Klitschko's stamina, setting up the painful denouement.
It was anyone's fight when Joshua landed the uppercut that proved decisive, much to the delight of his countrymen who packed England's national stadium for the highly anticipated bout.
"I'm a champion outside the ring, first and foremost".