Fury is due to challenge world titleholder Deontay Wilder for that sanctioning body's heavyweight world title belt December 1 in the main event of a Showtime PPV card at Staples Center in Los Angeles.
"If he does not enrol, then the WBC can not sanction the fight", Sulaiman exclusively told Sky Sports.
Fury is still not involved in a joint program from the WBC and vada - Clean Program Boxing Champions, contenders and fighters of the top 15 WBC ranking must undergo mandatory unannounced audit officers for WADA banned substances in the body, according to ESPN.
On Monday, Sulaiman announced that Fury had taken care of it.
"I can confirm Tyson Fury has now sent the clean boxing program enrollment forms to VADA testing", he told BoxingScene.com, in reference to the Voluntary Anti-Doping Association. "Now that Fury's paperwork is in and he is enrolled, we can start it nearly immediately".
Jaden Sancho admits England senior call-up was a surprise
He is snatching at chances, possibly because he is anxious about putting a foot wrong under José Mourinho. Rather they can "do a Sancho", go to another country entirely and potentially still be picked by England.
WBC president Mauricio Sulaiman said he was not aware that Fury had not enrolled in the program even though Fury should not have appeared in the WBC rankings until he had enrolled in the program.
The TV company have released footage of what was said after the cameras stopped rolling and as you can imagine, things got more than a little heated as the two giants once again looked to win the mind games ahead of the monster fight. I'm going to reach out to him, because there has to be testing for the fight, out of competition.
Wilder was present in Belfast in August to witness the Fury-Pianeta fight and focus quickly shifted from Fury's win to their potential clash as the American ace entered the ring moments after its conclusion.
Loud megafit in the heavyweight division between DevTeam Wilder (40-0, 39 KO's) and Tyson fury (27-0, 19 KO's) in jeopardy.