The 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."