The heavyweights reached a financial agreement earlier this year over what would be the biggest heavyweight fight in decades, and both have been trading barbs for some time now, increasing the hopes that an explosive encounter in the ring will finally come to fruition.
Fury's latest jibe comes in the aftermath of WBC president Mauricio Sulaiman publicly giving his backing to the showdown, praising both athletes and insisting his organisation will "absolutely support it" and help to make the all-British bout a reality.
Whyte and the Russian are set to meet in a rematch in January, with this month's scheduled second bout having been called off after Povetkin tested positive for coronavirus.
While the victor of that rematch could face Fury next year, Sulaiman told Sky Sports that he has great interest in seeing the champion take on WBA, WBO, IBF and IBO titleholder Joshua next.
Speaking this week to Sky Sports, Sulaiman said: "There's absolutely great hope from the world to see that undisputed fight".
It is expected that the same will happen with a location in the Middle East or Far East if the proposed Tyson Fury mega fight happens next year. Anthony Joshua holds the other belts and he has been a tremendous asset to the sport.
Joshua is due to defend his belts against Bulgaria's Kubrat Pulev on December 12 at the O2 Arena in London.
Fury meanwhile entered a mediation process over a disputed third fight with Deontay Wilder. There is no mandatory contender.
"We're just hoping that everything gets resolved and everybody is happy and we see great fights inside the ring".