The former IBF, WBA and WBO champion has not fought since his November 2015 defeat of Wladimir Klitschko, who was stopped in 11 rounds by reigning IBF and WBA champion Joshua at Wembley on Saturday.
He vacated the WBA and WBO titles he held last October after admitting using cocaine to cope with depression, after which the British Boxing of Control (BBBC) suspended his boxing licence.
That development came after an ankle injury had forced the postponement of his proposed rematch with Klitschko, and after Fury and his younger cousin Hughie were charged "with presence of a prohibited substance" by UKAD.
The 27-year-old Joshua's defeat of Klitschko, and the belief that still exists in some quarters that Fury remains the world's finest heavyweight, potentially makes a fight between the two rivals the biggest in British boxing.
Yet for all of their confidence in their chances of victory, the likelihood of that fight taking place will not become clearer until after the hearing with UKAD.
Press Association Sport understands the Fury camp are confident about the outcome for both Tyson and Hughie, and have targeted July 8 as the former's return. His friend and fellow traveller Billy Joe Saunders is set to defend his WBO middleweight title against Georgia's Avtandil Khurtsidze that same evening.
However even before that happens, he would also have to again be licenced to fight by the BBBC, another outcome they are confident about.
That return - before which Fury would need to lose a considerable amount of weight to be anywhere near his fighting shape - would be considered no more than a warm-up, as would at least his next fight.
Thereafter they hope to face an opponent of greater quality, potentially for a world title, and only from 2018 would a Joshua fight seriously become a possibility, a view Joshua's promoter Eddie Hearn shares.
Before then, there remain numerous obstacles for Fury to overcome, starting with Monday's hearing which Fury's promoter Frank Warren told Press Association Sport will not feature a reported defence of eating contaminated offal.
"It's totally untrue," Warren said. "There's no talk of any contamination at all; that's not the defence.
"That will all be determined on May 8. It's outrageous that these leaks are being made, irrespective of the outcome of the hearing.
"Tyson's training with Saunders; we want him to fight on that card, and he wants to fight on that card. If he gets an all-clear he'll fight on that show.
"Why shouldn't (the BBBC) give him his licence (if that happens)? If he's mentally and physically able to box there's no reason they shouldn't allow him to box. He's been having treatment.
"He's just turned 28: he's not an old man. He's lost a stone-and-a-half; he should lose weight very quickly provided he's training.
"I think he's mentally there. He should be in a good place so hopefully we can get him moving.
"He needs a couple of quick warm-up fights, and I'll make sure he gets them, then back into the swing of it."
