Fury, a committed Christian, is said to be "baffled" by the claims and his spokespeople have denied the allegations.
The Sunday Mirror claims UK Anti-Doping (UKAD) is overseeing the investigation but it refused to confirm or deny the claims.
Spokesperson Sophie Ashcroft said: "UK Anti-Doping does not discuss or disclose details of any cases until due legal process has been completed or a respondent chooses to put the information into the public domain.
"This is to protect the rights and privacy of all involved and to ensure that a case is not subjected to unnecessary prejudice.
"It is important to note that an anti-doping rule violation is only deemed to have been committed once the legal process, including any appeals, has been completed. At that point, details of a violation will be made available on the UKAD website."
The doping allegations are the latest controversy in a career which has frequently attracted negative publicity.
In the build-up to November's defeat of Wladimir Klitschko - which remains among the finest any British fighter has secured - he expressed extreme views on homosexuality and paedophilia.
He had told The Mail on Sunday: "There are only three things that need to be accomplished before the devil comes home: one of them is homosexuality being legal in countries, one of them is abortion and the other one's paedophilia."
Shortly after that victory, which he helped promote by dressing up as Batman, he was accused of sexism when revealing his belief that "a woman's best place is in the kitchen and on her back".
Police also investigated a hate crime allegation against Fury, when the strength of feeling towards him was so strong there were protests at his presence at the BBC's Sports Personality of the Year awards, where he apologised.
Since that apology, however, he has sparked further outrage when in an hour-long video posted last month he made homophobic, sexist and anti-Semitic remarks while being outspoken on rape and bestiality.
A statement from Fury's team read: "We are baffled by today's story in the Sunday Mirror. Tyson Fury absolutely denies any allegation of doping. He looks forward to recovering from his injury and defending his titles against Wladimir Klitschko in October.''
