Fury's latest remarks came after the 28-year-old made an abrupt U-turn on his retirement decision on Monday, tweeting: "I'm here to stay."
The British fighter recently cancelled an October bout with Wladimir Klitschko to defend his World Boxing Association and World Boxing Organization heavyweight belts.
Fury had been scheduled to earn the biggest purse of his career in a rematch with Klitschko at the Manchester Arena after shocking the Ukrainian last November to become world champion.
ESPN reported Fury tested positive after providing a urine sample to the Las Vegas-based Voluntary Anti-Doping Association (VADA) in Lancaster, England on September 22. Cocaine, while an illegal drug, is not banned in boxing if taken out of competition.
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Fury's camp made no comment on the reports of cocaine use but the boxer himself confirmed them in an interview that Rolling Stone said was conducted on Monday, before the champion's retirement U-turn.
"Why shouldn't I take cocaine? It's my life, isn't it? I can do what I want. Yeah, I have done cocaine. Plenty of people have done cocaine as well."
Fury, explaining why his re-match with Klitschko had been called off for a second time, said: "I've not been in a gym for months.
"I've not been training. I've been going through depression. I just don't want to live any more, if you know what I'm saying. I've had total enough of it.
Fury, in comments that appeared to suggest he had failed
a drugs test, also said: "I never took other drugs, ever, in my life. I only started to take cocaine in the last few months."
A member of the travelling community, Fury said he had been a victim of prejudice.
"It's been a witch-hunt ever since I won that world title," Fury added. "Ever since I got a bit of fame for doing good there's been a witch-hunt on me because of my background, because of who I am and what I do."
A previously scheduled rematch with Klitschko, set for July 9, was scrapped after Fury sustained an ankle injury.
Following the cancellation of that fight, it emerged that UK Anti-Doping (UKAD) had charged Fury and his cousin, Hughie, with a doping offence. They deny wrongdoing.
The sample, taken nine months prior to Fury's sensational victory over Klitschko, contained traces of the banned substance nandrolone.
Fury was provisionally suspended, but his ban has since been lifted and his legal team have threatened action against UKAD. He is due to face a hearing in November and could be stripped of his titles if found guilty.