Fury and Lewis have been involved in a spat over the past seven days, and the unbeaten fighter has insisted that the 47-year-old should not be talking about his ability to take a punch.
The 24-year-old told World Boxing News: "Lennox Lewis has the cheek to talk bout chins when he was proper chinny!
"He lost to journeymen, got knocked out too and I am unbeaten, what a bitch! I have no respect for him at all and David Price won't make nothing of himself as long as he is with Lewis."
Fury is currently in discussion to fight David Haye later this year.