Audley Harrison says Danny Williams is a failure and has vowed to finish his career when they meet at London's ExCel Centre on 10 December.
Last week, Williams predicted Harrison would quit in the biggest domestic heavyweight match-up since Lennox Lewis fought Frank Bruno in 1993.
Harrison said: "I have never quit, so Danny is in for a rude awakening.
"Danny's an underachiever. Whenever the time has come for him to step up and show what he's got he has failed."
Williams claims Harrison attempted to bail out when they sparred five years ago, when Harrison was an amateur and before he won Olympic gold in Sydney in 2000.
In reply, Harrison has taunted Williams for pulling out of a fight with current British champion Matt Skelton in July.
"I hope he does not pull his notorious Matt Skelton disappearing act - quitting before he even got to the ring that night," said Harrison, who is unbeaten in 19 professional fights.
"Danny Williams can reflect all he wants on the past, although his memory might be jarred from the beating he took from [Vitali] Klitschko last December.
"I refuse to lose to a club fighter such as Danny Williams because that's all he is. After my beating Danny, you really should consider hanging up your gloves."