Joshua was putting his International Boxing Federation, World Boxing Association and World Boxing Organisation belts on the line against 39-year-old Russian challenger Povetkin.
Parker, of course, failed to build on the profile he received in the United Kingdom from their title fight by succumbing to a second successive unanimous points defeat to Dillian Whyte in August.
Hearn may well have his work cut out selling a Whyte Pay-Per-View if Joshua doesn't manage to seal a fight with Wilder or Fury next.
Joshua's next fight will be on April 13 back at Wembley Stadium and while WBC title holder Deontay Wilder remains the favourite, a domestic dust-up with Tyson Fury or a re-match with Dillian Whyte are also on the cards.
"There is a lot of pressure, the whole country is rooting for me", said Joshua, who enjoys a wide popularity, having drawn nearly 400,000 spectators to his last five fights combined. "If Fury beats Wilder, that fight against Joshua becomes even bigger than we're talking about".
Wilder, who is scheduled to defend his WBC title against Tyson Fury at a venue yet to be decided in the USA on 1 December, has gone the distance once in 40 fights and owns what is regarded as the single most powerful right hand in the division.
"I know Anthony Joshua has made his shopping list of who he would like to fight next and that is Deontay Wilder, but that is not to say the deal can be done".
"I believe Tyson Fury will be the victor of that fight so why on earth would anyone want to stand in its way?" added Warren.
"13 April is what I'm really interested in".
Anthony Joshua opened a poll for his next opponent on Sunday and within minutes had nearly 60,000 votes.
Only Joseph Parker has interrupted Joshua's run of early finishes and the champion was pleased to win by stoppage for the 21st time. "He is slow, methodical, ponderous at times, powerful yes, but they all are". Deontay Wilder is not going to risk his title without a rematch clause.
"Sometimes you have to face your mandatory challenger, and now that's out the way we will put a poll out for who the fans want". "Good luck to Wilder".
Only then will we truly know who just who is the best heavyweight on the planet.
The venue and date of Joshua's next fight have always been determined - Wembley Stadium on April 13 - but the opponent is still unclear.
"Let's see if Wilder v Fury actually happens". When they're ready we're ready...
That an estimated 68,000 were present at Wembley Stadium - significantly fewer than the 90,000-strong crowd that attended last year's victory over Wladimir Klitschko - demonstrated that, but he professionally overcame an opponent of ambition and class.
He got up, somehow, but another flurry from Joshua was enough to end it.