The 40-year-old heavyweight, who had previously announced his retirement from the sport, unsurprisingly triumphed against his friend Joe Fournier in Saturday night's fight (11/9/21), and immediately turned his attentions to Fury.
He said: "There's one fighter I'd come back to professional boxing for.
"That's Tyson Fury.
"That big fat dosser, I know his kryptonite, I know what he can't handle.
"He wants a fight?
"'The Hayemaker' will come for you.
"When Tyson Fury really wants a challenge, the fans want to see it, the fans want to see Tyson Fury facing someone who can knock him out.
"I know that he knows it, his dad knows it, his uncle knows it."
Haye had been due to fight Fury twice previously but was forced to pull out o both occasions because of injury.
And the 40-year-old Londoner says he's been eyeing up a fight with Fury since 2013.
He added: "It's been in my mind for a long time, since 2013.
"The fight didn't happen, I got an injury.
"I've always wanted that fight.
"I've seen him get better and better.
"His reputation has got bigger and bigger.
"If I'm going to come back into boxing with a real fight, against someone special?
"That is the guy I know I can beat.
"I know his style.
"I know what he does well.
"My attributes don't work well for his style.
"Him and his team know that.
"I'm looking for the biggest fight out there - and you get no bigger than 6ft 9in Tyson Fury.
"I'd only come back for Fury.
"I don't want to show him what I've got left.
"I was able to win this fight without showing 'the Hayemaker'."
And having come through Saturday's bout relatively unscathed Haye feels ready "to do big things".
He said: "I felt fresh, smart, my timing was good.
"Normally I knock people out straight away but I enjoyed myself.
"I could see shots coming but I hadn't done much sparring for this.
"I've hurt my body over the years.
"I needed rest.
"I needed my body to rejuvenate.
"I'm ready to do big things."