Kinahan was last week named as being a head of the Irish Kinahan crime gang and hit with worldwide financial sanctions by the United States Government.
"Whilst visiting Dubai recently I was introduced to Daniel Kinahan, who has since been placed on a sanctions list by the US Treasury Department, concerning alleged links to drug crimes," said Sulaiman.
"This has generated speculation and attacks on myself and the WBC. I therefore feel it necessary to make it clear that at no time have we had any relationship with Daniel Kinahan.
"The World Boxing Council deals solely and exclusively with boxing promoters and only they maintain commercial relations in the certification of fights for our titles.
"The WBC has had for many years a large number of social responsibility campaigns focused on the prevention and awareness of the dangers of drug use.
"We have a wonderful program of talks given by a former DEA agent, Rocky Heron, who reaches thousands of people with his presentations. We have rescued many boxers and members of the boxing community around the world from the demons of addiction and we openly and constantly support rehabilitation clinics such as those of Julio Cesar Chavez and Aaron Silva, among others.
"I made an innocent mistake, due to absolute ignorance of the situation. In this way, I confirm that the World Boxing Council and all its members absolutely reject any action that is detrimental to human beings and we will continue, as always, in total compliance with the laws of all countries in the world."
Kinahan was a co-founder of the MTK Global agency, which represents a number of boxing's leading fighters, including Fury.
He says he cut ties with the company in 2017, but the world of sport was warned over its involvement with the Kinahan organised crime group after US sanctions were put in place.
There is no suggestion of criminality by any of the fighters advised by Kinahan.
US authorities have offered a five million dollars (£3.84m) reward for information on the three most senior members of the Kinahan organised crime group - Christy Kinahan Snr and/or his sons Daniel and Christopher Jnr.
Asked about Daniel Kinahan's role in the Fury-Whyte fight, Warren told the BBC Radio 5 Live boxing podcast: "He has no involvement. Nor did he try to get involved in this fight because it was a purse bid.
"Queensberry won the purse bids and, even if we hadn't won it, he wouldn't have been involved."
It was reported that Bob Arum's Top Rank paid fees of 1.5m-2m dollars (1.1m-£1.5m) to Kinahan for Fury's past four fights.
But Warren said: "We knew nothing. I certainly knew nothing and I know Tyson knew nothing about the payments made by Top Rank to the company in the Middle East.
"Tyson was unaware. He'll speak for himself but I know for a fact he was totally unaware of those payments.
"That's their business. It's nothing to do with us. Certainly nothing to do with me and, as I say, Tyson was unaware of it."