Fury believes that Price has taken an easy option by signing up to fight the 40-year-old Harrsion in October.
Fury told World Boxing News: "Audley's an old man and washed up, even in his prime he had no guts.
"Price has been managed so well his team should be called mothercare. He's never been even remotely tested as a pro so don't buy the hype."
Price will defend his British and Commenwealth titles against Harrsion at the Echo Arena in Liverpool on October 13.