The 36-year-old was quick to respond by saying that it would be "an easy night's work" if Bellew stepped up to heavyweight to fight him.
Bellew, 33, told Sky Sports News on Sunday: "The last two guys he has fought (Mark de Mori and Arnold Gjergjaj) are a joke. One was called 'The Cobra', he should have been called 'The Worm', and the other fella was an internet-trained boxer.
"Come and fight a real world champion. I am the best cruiserweight in the world and let's be totally honest here, David Haye isn't a genuine, legitimate heavyweight. He's originally a cruiserweight, he once had this belt and now I'm saying I'm the best cruiserweight in the world.
"If you don't want to come back to your old weight no problem - you might be scared to come back down to your old weight - but I'll happily step up. I enjoy my food and I will enjoy punching him in the face."
Haye, previously tipped to face Anthony Joshua at some point this year, is next scheduled to fight on December 10.