It was a fight that reached new depths in terms of poor behaviour in the build-up from both fighters, who had to be physically separated at the weigh-in, but it served to hype a grudge match which sold 890,000 pay per views in the UK and finished with a dramatic 11th-round TKO for the smaller Bellew after Haye injured an Achilles tendon in the sixth.
Bellew, who fought at a career-heavy 96.8kg, broke his right hand during the fight and considered retirement before carrying on. A rematch with Haye is possible but a world title is a bigger attraction.
"Joseph Parker is a dangerous, live, little heavyweight among huge giants," Bellew said. "That's what he is in my opinion ... he's a dangerous small heavyweight, who I do like the look of, if I'm totally honest.
"I like the sound of world heavyweight champion, it's got a nice ring to it, but we will have to see, we will see what Joseph Parker wants. It is out of the question for me to go to New Zealand, Australia, anywhere close to that is out of the question."
Asked about Parker having to fight him in the UK, Bellew said: "Listen, British boxing is now the home of world boxing."
The fanatical Everton supporter, who won his world title at the football club's Goodison Park ground last year, would like the idea of fighting there again.
"It's a fight that I do like, I'm not going to lie to you, but there is going to have to be some negotiating done. I have got respect for Joseph Parker, I do think he's a good fighter, but let's not mix this up.
"He's had his whole career campaigning at heavyweight, I've had one fight at heavyweight, and my whole career at heavyweight is better than Deontay Wilder and Joseph Parker's careers put together.
"These two guys wouldn't even mutter the name David Haye. They don't even whisper it in the dark because they're scared he might come out. I took on the monster, I defeated the monster against all the odds, and believe it or not, against all the odds, which I would be against Joseph Parker, I will beat him. Boy, you keep on saying my name, if I put my name, and sign that contract, your title reign is over, it's as simple as that."
Bellew, a 34-year-old who starred in the Rocky movie Creed, added: "I'm the better boxer, I'm slicker than him, I'm cleverer than him, my footwork is far better than his.
"He's stronger, he's definitely younger. He does look like a bit of a specimen. He's another guy who I look at and aesthetically he looks fantastic, doesn't he? He reminds me of the great rugby player when I look at him."
"Jonah Lomu? Yes, he reminds me of him.
"Listen, we will sit down, we'll talk ... and if you want to dance with me, then you better show up well prepared because I have shown what I do to fighters who don't show up well prepared. I deal them a bad hand and it could just be the end of him, so choose carefully, boy."
