Price knocked out Audley Harrison in just 82 seconds on Saturday night to retain his titles, but domestic heavyweight rival Fury was far from impressed.
Fury launched a scathing attack on Price from ringside at James DeGale's European title defence later that night.
He said: "It's real personal between me and you, I'm gonna do you some serious harm you big, stiff idiot.
"You are getting it for sure, I'm going to put you in intensive care."
Liverpudlian giant Price told Sky Sports News that he pays no attention to the insults, but admitted that he is still desperate to fight Fury.
Price said: "He's round the bend. I don't know what to make of that.
"He cannot handle other people getting praise and credit and that's why he spat his dummy out on TV and made an absolute fool of himself by the sound of it.
"Of course it's a fight that I would like. The fight was ready to be made earlier on this year but they obviously didn't want it."
Price is back in action in December against British veteran Matt Skelton for a fight likely to take place at Aintree racecourse.