Klitschko, 38, defends his belt against unheralded American Kevin Johnson in Berne, Switzerland tomorrow.
And Haye, who won the WBA title from Russian giant Nikolay Valuev last month, is keen to meet Klitschko in the ring before age catches up with him.
“Vitali is nearly 40 years of age now and the clock is ticking,” said Haye.
“There are probably one million dudes in America called Kevin Johnson, and beating one of them doesn’t make you an all-time great heavyweight. “Vitali’s greatest performance to date is a loss to Lennox Lewis. That’s his most memorable fight and the one result on his record that will be remembered in the history books.
“The Klitschkos (Vitali and brother Wladimir) don’t care about being great fighters, whereas I do.
“They may be big in Switzerland, but so are yodellers, and nobody wants to watch them fight.
“It’s one of the most unappealing heavyweight title fights for a while, and that’s saying something.”
Londoner Haye, 29, has long craved a showdown with Klitschko or his younger brother Wladimir, the IBF and WBO champion.
And after making a mandatory defence against two-time heavyweight world champion John Ruiz early next year, the Briton is determined to secure unification fights.
“I want to knock out both Wladimir and Vitali Klitschko, and I don’t care what order they fall in,” said Haye.
Vitali outclassed unbeaten American Chris Arreola in his last defence in September while Johnson should represent an even more straightforward task on Saturday.
“I’ll be watching the fight, but only because I have an interest in meeting Vitali next year,” said BBC Sports Personality of the Year candidate Haye.
“The fact that a title fight between a Ukrainian and an American is being held in Switzerland tells you all you need to know about the appeal of this fight.
“Heavyweight title fights should be huge events, not an after-thought in a country most famous for producing Toblerones.” — BBCOnline.