But tensions boiled over when Haye appeared to land a blow on Bellew before security staff stepped it to separate the pair.
Haye had earlier mocked Bellew by claiming he could knock him out while "drunk out of my head".
He said: "You and your whole team are going to get destroyed.
"Whatever I do now in my life is irrelevant because on fight night, you're going to get knocked out.
David Haye appeared to punch Tony Bellew at a heated pre-fight press conference
“I will turn up, drunk out of my head, and you'll get knocked out”David Haye's message to Tony Bellew
"I could go clubbing every night. From now until the fight, get smashed out of my mind every night, and I'll still knock you out.
"I will turn up, drunk out of my head, and you'll get knocked out."
Current WBC cruiserweight champion Bellew revealed he’s already bowed down to several demands from Haye to make the fight happen.
The Scouser said: "He's got this thing that I'm scared of him. All those demands, all those stipulations you put in.
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"'I want the ring this size, I want the mat that size'.
“Listen mate, I'm not going to run from you. I know you believe I'm going to run.
"All these stipulations he put in, I'm surprised he didn't ask me to carry him to his seat in the press conference, to be honest.
"Do you want me to do your hair as well? The man is unbelievable. My demand was - let me pick my own gloves and get in the ring.
"He's unbelievable - the biggest diva in boxing I have ever seen."
