The 35 year-old has been linked to facing both over the past few months, and after being part of constant speculation, Haye has finally broken his silence on whether he would accept a fight with either of his UK rivals.
“Ideally, I’d like Joshua. He is the guy who, in my opinion, is the most dominant heavyweight out there currently,” Haye told Sky Sports News HQ.
“He is the guy who hasn’t put a foot wrong and he is the guy that’s making the most noise. Obviously being from Britain myself it’s the biggest fight.
“I’m in boxing for the biggest possible fights and getting a belt around my waist is exactly where I want to be.”
On the possibility of taking on Bellew, who recently launched at Haye when ringside at the Echo Arena, the Londoner added: “A lot of people are stopping me and wishing that I smash him up so badly that he can’t keep screaming and shouting, so it is interesting.
“I didn’t think, the fact that he was a cruiserweight, that people would really consider it a serious fight but they are considering.
“People really want to see him get battered that badly. People in boxing now are used to fighters jumping through weight divisions to make the fights that the fans want to see and if the fans want to see it then I’m definitely interested in it.
“As I said, I will knock him out with a jab, and I stand by that, it wasn’t just a flippant comment, I’ll genuinely knock him out with a jab. I’d like it to happen, whether he wants it to happen or not is a different thing.
“There is saying you want to fight someone and then there is actually fighting someone – two completely different things – and he’s never been hit anywhere close to being hit as hard as I can hit so I think he might have talked himself into getting violently knocked out.”