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7 year oldThe leaked US Anti-Doping Agency (Usada) report, dated March 2016, was obtained by the Sunday Times.
"If Usada or any other anti-doping body has evidence of wrongdoing they should publish it and take action rather than allow the media to be judge and jury," said Farah, who has won 5,000m and 10,000m gold at the past two Olympics.
The coach in question, Alberto Salazar, has been under investigation since a BBC Panorama programme made allegations about drugs use at his US training base.
According to the Sunday Times, the leaked report also alleges Salazar, head coach of the world famous endurance Nike Oregon Project (NOP), routinely gave Farah and other athletes legal prescription drugs with potentially harmful side-effects without a justifiable medical reason.
The investigation into Salazar, who is also a consultant to UK Athletics (UKA), has been under way since at least June 2015.
Salazar and Farah deny they have ever broken anti-doping rules.
"It's deeply frustrating that I'm having to make an announcement on this subject," said 33-year-old Farah in a statement.
"I am a clean athlete who has never broken the rules in regards to substances, methods or dosages and it is upsetting that some parts of the media, despite the clear facts, continue to try to associate me with allegations of drug misuse.
"I'm unclear as to the Sunday Times's motivations towards me but I do understand that using my name and profile makes the story more interesting but it's entirely unfair to make assertions when it is clear from their own statements that I have done nothing wrong.
"As I've said many times before we all should do everything we can to have a clean sport and it is entirely right that anyone who breaks the rules should be punished."
In a statement UK Athletics said it stood by the findings of an investigation published in 2016 that found "there was no evidence of any impropriety on the part of Mo Farah and no reason to lack confidence in his training programme".
The statement said: "Usada have not reported back to UKA on any aspect of their investigations but we remain, at all times, completely open and cooperative with them.
"L-carnitine is a legal and scientifically legitimate supplement that can be used by endurance athletes. To our knowledge, all doses administered and methods of administration have been fully in accordance with Wada-approved protocol and guidelines."
The Usada interim report was passed to the Sunday Times by the suspected Russian hacking group Fancy Bears.
The BBC has so far been unable to verify its authenticity with Usada, or establish whether any of its reported conclusions are out of date.
In a statement, Usada said it could "confirm that it has prepared a report in response to a subpoena from a state medical licensing body regarding care given by a physician to athletes associated with the Nike Oregon Project".
It said: "We understand that the licensing body is still deciding its case and as we continue to investigate whether anti-doping rules were broken, no further comment will be made at this time.
"Importantly, all athletes, coaches and others under the jurisdiction of the World Anti-Doping Code are innocent and presumed to have complied with the rules unless and until the established anti-doping process declares otherwise. It is unfair and reckless to state, infer or imply differently."
Contents of the report
According to the Sunday Times, the leaked report claims that Salazar:
Salazar maintains that drug use has always fully complied with the Wada code and that athletes were administered with L-carnitine in "exactly the way Usada directed".
The Sunday Times claims the Usada report also reveals:
The report, apparently written in March 2016, allegedly states: "Usada continues to investigate circumstances related to L-carnitine use" by Farah.
Farah told the Sunday Times two years ago that he had "tried a legal energy drink" containing L-carnitine but "saw no benefit" and did not continue with it.
The newspaper also claims the report says Dr John Rogers, a medic for the British athletics team, told Usada in an interview that conversations he had with Salazar at a training camp in the French Pyrenees before the 2011 World Championships in Daegu, gave him such "concern" that he wrote an email at the time to his medical colleagues at UK Athletics.
It also says Rogers told Usada that Salazar had told him about "off-label and unconventional" uses of the prescription medications calcitonin and thyroxine (hormones) and high doses of vitamin D and ferrous sulphate.
The revelations will pile more pressure on Britain's greatest ever endurance runner, who has steadfastly refused to end his association with Salazar.
It raises questions too for UKA, which gave the Briton the all-clear to continue working with Salazar after an inquiry was launched following the BBC Panorama programme.
Background
In June 2015, in conjunction with the US website ProPublica, the BBC's Panorama programme Catch Me If You Can made a series of allegations about the methods at NOP, and included testimony from a number of former athletes and coaches, including Kara Goucher and Steve Magness.
The film alleged Salazar had a fixation on the testosterone levels of his athletes, and may have doped American Olympic medallist Galen Rupp with the banned steroid version when he was 16. The programme also alleged Salazar had conducted testosterone experiments on his sons to see how much of the drug he could apply to them before it triggered positive tests.
The film also alleged Salazar used thyroid medicine inappropriately with his athletes, and encouraged the use of prescription medication when there was no justifiable need.
Salazar denied the wrongdoing alleged in the programme, and issued a 12,000-word rebuttal.
Usada took the unusual step of confirming it had launched an investigation into NOP following the BBC and ProPublica's revelations in 2015. Earlier stories by the New York Times and the Sunday Times had also raised concerns about some of Salazar's methods.
It is not clear why the Usada report remains unpublished.
The BBC has sought comment from Alberto Salazar and UK Athletics.
BBC sports editor Dan Roan
Nine months ago, amid rumours Usada had dropped an investigation into his coach, Sir Mo Farah said he felt vindicated after standing by Alberto Salazar, the man who has helped him achieve so much success. This will raise more questions over that association.
Last year Farah distanced himself from another controversial coach - Somalian Jama Aden. And he could now face renewed pressure to do something similar with a man who we now know Usada is still looking into.
This could also be awkward for Salazar's employers Nike - and for UK Athletics; not least how they came to clear Salazar in 2015 - even though it now seems one of their senior medics - Dr John Rogers - says he had raised concerns to them over the coach's methods.
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