Fury has not fought since sensationally beating Wladimir Klitschko in Dusseldorf two years ago to claim the IBF, WBO and WBA heavyweight titles.
The 29-year-old gave up his belts last year amid a battle with mental health issues and had his licence revoked after allegations of a failed drugs test.
British Boxing Board of Control general secretary Robert Smith said Fury's UK Anti-Doping (UKAD) hearing can resume when his legal team agree a date.
A licence will not be reinstated until that hearing has taken place, but the Englishman has called out his compatriot Joshua, the WBA and IBF champion, for a fight which he compared to the Rumble in the Jungle between Ali and George Foreman.
Fury also has his sights on WBC title-holder Deontay Wilder
A post shared by Tyson Fury (@gypsyking101) on Oct 30, 2017 at 5:28pm PDT
He posted a picture of Ali and George Foreman in the ring in 1974 on Instagram and wrote: "This is what's to come! The old champ coming back to fight a man who every1 thinks will ko me, same as Ali vs Forman [sic].
"The stylish Ali vs the mummy Forman! [sic] We all know what happens in this fight! I know you all got me whooped, but I will not lay down or be afraid of some muscles & I have the mentality of a winner a man who has never lost a fight.
"A true champion coming back to claim his thrown [sic], This is my era they are from my time, I must destroy them. AJ & Wilder I'm coming back for you pair my mission is seek & destroy the only thing on my mind is destruction whoever gets in my way will be dealt with accordingly.
"There's only 1 winner & that's the fans! Let's make the heavyweights great again, fight the best in the division, Fury= Lineal champ, Joshua= Ibf-Ibo-wba Wilder= WBC. Parker= Wbo But to be fair Parker is only a young lad & is not on my radar he must gain experience & mature in to a big strong man.
"I hold my destiny in my own hands. May the best man win good luck everyone #letsgetthispartystarted2018_2019 the world will see the best fights & see the true heavyweight king recrowned."
A post shared by Tyson Fury (@gypsyking101) on Oct 31, 2017 at 3:59am PDT