Apparently overlooking the merits of Muhammad Ali, Larry Holmes, Lennox Lewis and many other heavyweight greats from considerably more decorated eras, the former British and Commonwealth champion also reiterated his desire to fight Haye, even if many of his brags are not to be taken seriously.
The two have been negotiating about a potential fight for some time with Haye adamant that his rival cannot expect more than an even share of the purse but with progress appearing to stall and Haye making his frustrations public, Fury has set an imminent deadline on the two agreeing terms.
'Arrogant': Tyson Fury has made no secret of his dislike for David Haye
'We have a deadline of the end of the month to sign a contract, so if he wants a fight he will sign the contract. If not we will move on, but it is never over until it is over and there is room for negotiation and I am sure we can reach an agreement.
'Me and my team are optimistic about the fight, I hear Haye's team are optimistic.
'So I don't see why this fight should not happen. He wants to fight, I want to fight so it should be done soon enough.'
Tenacious: Fury has repeatedly shown his fighting heart, including in his recent win against Steve Cunningham
Natural fighter: But Fury has dismissed Haye as a 'has-been'
Left jab: Haye has held world titles at both cruiserweight and heavyweight
By way of comparison, however, Haye has been inactive for just under a year when he won in five against Dereck Chisora, an opponent who took Fury the 12-round distance, and as with Haye's fights with Chisora and Wladimir Klitschko before then there appears a genuine dislike between he and Fury, who also delivered an almost-routine threat.
'There is animosity there as I genuinely don't like the fella,' Fury said. 'He is arrogant, he thinks he is everything and really he is just a pumped up cruiserweight who has not fought anybody.
Loud and proud: Fury is one of the best trash talkers in boxing
'You are not as good a mover as Steve Cunningham, so I will blast you out.'