The Manchester born boxer, who holds the WBA and WBO world titles, was informed his A sample from a random urine test on 22 September had tested positive for the substances found in cocaine.
The 28-year-old could now be stripped of his world titles, should a B sample also test positive for the drug.
Team Fury are clinging to the hope that their boxer will be granted a delay before action is taken so that he might have the chance of a third attempt at a rematch against Klitschko next year.
But the alpha belt bodies, who finance their operations from their sanctioning fees for championship bouts, are unlikely to allow Fury to retain his belts following his two previous withdrawals.
Klitschko, meanwhile, is in negotiations to challenge Anthony Joshua for his IBF title in Manchester at the end of November.
However, his team has booked a football stadium in Germany for December 10, in anticipation in him being granted a challenge for Fury's belts, should they fall vacant.
The retrieval of the majority of the titles he held for a decade is Klitschko's preferred option and the Ukrainian's agent, Bernd Bonte, confirmed they are monitoring the situation surrounding Fury.
'We are in talks with Eddie Hearn for a possible fight with Joshua but we are waiting developments,' he said.
Fury's failed drugs test is the latest in a number of controversial incidents throughout the British heavyweight's career.
In 2015, prior to his first fight with Klitschko, Fury compared homosexuality and abortion to paedophilia in an interview.
The following year a video emerged of Fury calling transgender people 'freaks of nature' whilst claiming that rape and bestiality will one day be made legal.
The WBA are yet to make a decision whether to strip Fury of his belt and are awaiting the results of the fighter's B sample.
'The Committee of Champions will consider Fury's case to make a decision,' the WBA said in a statement released on Friday evening.
'Regarding the VADA report, they sent a statement in which they inform that the result was positive. Now we are waiting to see if Fury's team will request the opening of the B sample test.'
