Fury has been in talks to defend his WBC heavyweight championship against mandatory challenger Whyte.
“I’ll give him the best hiding he’s ever had.
“Whyte, train hard! Because you are getting annihilated.”
Fury had previously hinted that Joshua had chosen to go ahead with a second fight against IBF, WBA and WBO champion Usyk, instead of opting to step aside and fight the winner of Fury vs Usyk.
“Joshua and [his promoter] Eddie Hearn are the worst businessmen in history – today they lost $90m,” Fury claimed.
The WBC confirmed on Wednesday that the free negotiation period between Fury and Whyte would be extended for the final time until Friday January 28.
If a deal has not been privately struck, purse bids will then be made – enabling any promoter to enter the negotiations and finance the fight.
The WBC previously ruled that Fury should keep 80 per cent of the total earnings from a fight with Whyte.
Whyte remains in arbitration with the WBC.
Up coming Boxing schedule
Sunday January 30 in Tulsa
Robson Conceicao vs Xavier Martinez – WBC super-featherweight title eliminator
Nico Ali Walsh
Saturday February 5 in Cardiff
Chris Eubank Jr vs Liam Williams
Claressa Shields vs Ema Kozin – IBF, WBA and WBC middleweight titles
Saturday February 19 in Manchester
Amir Khan vs Kell Brook
Frazer Clarke’s pro debut
Saturday February 26 in Glasgow
Josh Taylor vs Jack Catterall – undisputed super-lightweight titles
Nick Campbell vs Jay McFarlane – Scottish heavyweight title
Saturday March 5 in Fresno
Jose Ramirez vs Jose Pedraza
Sunday March 20 in New York
Edgar Berlanga vs Steve Rolls