At the time, last summer, Conde Nast and Mr Fayed were locked in the most ferocious of legal battles, arising from a lengthy article published in September 1995 in Vanity Fair, one of Mr Coleridge's stable of magazines, detailing the Harrods tycoon's private peccadillos.
Mr Coleridge was growing more confident of winning the libel action, of having collected enough material on Mr Fayed to see him off. This, he knew, Mr Fayed and Mr Cole, his loyal lieutenant, also realised. But if the offer of a meeting, presumably to broker peace, was not a surprise, then the suggested choice of venue and clothing certainly was: the Turkish bath at The Bath & Racquets Club in London's Mayfair; dress naked.
Such was the paranoia of both sides in this multi-million pound libel action that had occupied dragoons of lawyers and private investigators in London and around the world for the best part of two years, that Mr Coleridge acceded to the proposal. His suspicion was justified: previously, a colleague had been approached by someone purporting to have information on Mr Fayed; the colleague agreed to pay him, only to discover he was still a Harrods employee and it was a sting. A complaint was duly made to the police, alleging Vanity Fair had been trying to bribe Mr Fayed's staff.
By appearing naked, said Mr Cole, his adversary could rest assured he was not being recorded - likewise, it occurred to Mr Coleridge, his enemy could also speak in the knowledge he was not being taped. So they met, stark naked, in the Turkish bath of Mr Cole's London club.
They sat on a marble slab and amid the heat and steam, sweating profusely, Mr Cole made his overture: it was time, he said, for the two companies, Harrods and Conde Nast, to settle their differences; as leading players in the luxury goods market, they should be working together, not against each other. The action, both men knew, was threatening to consume millions of pounds in legal costs, not to say thousands of hours of executive time.
Money, though, was not the issue. Sure, the Harrods camp was huffing and puffing about seeking damages in excess of pounds 1m, and the costs were mounting. But Mr Fayed sits on assets worth hundreds of millions and Conde Nast is owned by SI Newhouse, one of the richest men in the world - even wealthier than the Harrods owner.
It was a high-stakes battle about pride and reputation - destined, if it went to court, to be one of the most celebrated libel trials ever - that neither side could afford to lose. Mr Fayed, proprietor of the most prestigious store in Britain, if not the world, possessor of royal warrants and friend of the rich and famous; Vanity Fair, the most sophisticated of titles, renowned for quality writing and rigorous fact-checking.
Mr Cole's offer came after Vanity Fair had submitted its defence. Mr Coleridge's response was cautious - they had been down this road before, when Harrods suggested talks soon after the article first appeared, only to find Mr Fayed was thinking in terms of an apology running to two pages.
He was right to be cautious because Mr Fayed's mood suddenly hardened. The Egyptian multi-millionaire became bullish and buoyant. The reason, it was not hard to fathom, was the blooming romance between his son, Dodi, and the Princess of Wales. For Mr Fayed, this was a crowning, happy period with a clear, underlying message of him putting one in the eye for the conservative establishment he despised so much.
August, however, proved to be a terrible month. First, before a judge in chambers in Norwich, Vanity Fair submitted a re-amended defence, stronger than the first, full of compelling evidence. Then, at the very end, Dodi and Diana were killed.
In an instant, the ebullience and swagger evaporated. His mood was not helped by a change in media coverage, from one of sympathy to ridicule after it was revealed that their driver and his employee, Henri Paul, had been drunk. Claims from Mr Cole that the paparazzi were to blame for the deaths and that Mr Fayed had received notification of the Princess's final words, were also traduced in the press.
Bert Fields, Mr Fayed's redoubtable US lawyer, whose clients have included Michael Jackson, John Travolta, Warren Beatty, the Beatles and Dustin Hoffman, and goes by the nickname of "The Pitbull", was instructed to negotiate a settlement. That has now been made. Vanity Fair will make no apology, no retraction. If Mr Cole tries to maintain the magazine made any concessions on accuracy it is sitting on a mound of material damaging to the Harrods owner - and Mr Newhouse (Mr Coleridge would not be interviewed for this article) is in no mood for backing down.
Mr Fayed is in danger of falling out with his closest media ally. He has been railing in private against the Guardian, which followed up his stories of Tory MPs on the take. The newspaper, he believes, has not done enough to thank him. He has asked that it should pay pounds 500,000 towards his legal costs arising from the cash for questions saga.
Perhaps Alan Rusbridger, the paper's editor, will shortly receive an offer to join Mr Cole in the Turkish bath.