Dennis, the millionaire behind Dennis Publishing which launched men's magazine Maxim and The Week, made the claim on tape in a five-hour, wine-soaked interview with writer Ginny Dougary at his house several months ago.
In the published interview, Dennis claimed he pushed a man off a cliff around 25 years ago, because he was beating up a woman he knew and her kids.
Dennis said: "He hurt her and I told him to stop and he kept on... Many people told him to stop. Wouldn't stop. Kept on and on and on. Made her life a living misery: beat her up, beat up her kids, wouldn't let her alone, kept on, kept on -- weren't even her kids... so in the end, I had a little meeting with him, pushed him over the edge of a cliff. Weren't 'ard."
Dougary then asked Dennis, "Are you sure you want to be telling me this?", and Dennis said, "Don't care. Anybody harms one of mine... if they harm one of mine, they'd better know what they are doing."
However, the next morning he emailed Dougary to thank her for the enjoyable afternoon and evening, and to suggest she "forget one particular episode I recounted to you after the third or fourth bottle in the conservatory".
In a later letter to The Times' editor, months after the interview, he explained his doctor had reminded him that at the time of the interview he was suffering from a form of anaemia and thyroid imbalance, for which he had been prescribed Prednisolone and Carbimazole, which taken with large amounts of alcohol can cause mood swings, severe exaggeration and a kind of manic or psychotic behaviour.
A spokeswoman for Dennis said: "There is no comment -- this is a ridiculous story."
It would be an understatement to say Dennis, who has built up a fortune of around £750m and has five homes, has a chequered past.
He was convicted for obscenity in 1971 as one of the founders of underground magazine Oz before the verdict was overturned on appeal. He has also admitted to crack cocaine binges and using prostitutes.
More recently, he has written and , a bestselling book 'How to Get Rich' and is spending a large part of his fortune on planting a forest in the UK called the Forest of Dennis.
Last year, he pocketed around £121m by selling the international editions of Maxim magazine and its brand extensions, and US magazines Stuff and Blender, to private equity firm Quadrangle Group.
A Metropolitan Police spokeswoman said they would need to know where the supposed crime happened before they could decide whether to investigate.