Negotiations between the two sides, which have been in dispute for two years, were at an advanced stage when they broke up late on Friday evening. Mr Fayed was believed to be ready to settle without an apology or retraction for a 1995 article, detailing allegations about his sexual and private life.
Still being discussed is the responsibility for the costs of the myriad lawyers and investigators from both sides involved in the case, which was proving to be one of the most expensive ever brought in this country. Mr Fayed is expected to have to meet at least some of the costs of Vanity Fair and its publisher Conde Nast, thought to be well in excess of pounds 1m.
The climbdown will be a humiliation for Mr Fayed, who threatened all manner of retribution against Conde Nast, Vanity Fair editor Graydon Carter and article author, Maureen Orth. It comes after the US-based magazine last week published another article, this time on the private life of his late son, Dodi. Mr Fayed is believed to be have asked his lawyers to see if Vanity Fair slipped up in the Dodi article, which detailed his son's cocaine habit, with a view to making a claim for aggravated damages. But his lawyers concluded there were no grounds for Mr Fayed adding to his claim.
The offer to settle may also have been influenced by a court hearing, due tomorrow. Vanity Fair was to apply to be allowed to use evidence from an earlier, failed legal case brought by Mr Fayed against Christoph Bettermann, his former number two at Harrods. Mr Bettermann claimed Mr Fayed bugged staff, while his wife, Francesca, who was Harrods' in-house lawyer, said she had to take an HIV test and have her handwriting analysed before joining the store's senior management team.
Mr Fayed sued the magazine on four counts, claiming the article accused him of sexual harassment, racism, being obsessed about personal hygiene and ill-treating staff. On all four, he is now prepared to throw in the towel.
Nobody from Conde Nast was available to comment on the case yesterday. A Harrods spokeswoman said she could not comment on the case.
Mr Al Fayed's plans for a 20ft tall red granite tomb for his son, Dodi, in the grounds of the family estate in Oxted, Surrey, are on hold pending a council inspection. The body was moved to the estate from the cemetery where he was originally buried in Woking as his father wanted him to be close to the family.
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