Solicitors Leigh Day, which represents the claimant, has previously said it had been contacted by more than 100 women.
A separate legal case is being brought by the Justice for Harrods Survivors group, which has previously said it is representing more than 400 women.
Al Fayed, who died aged 94, owned Harrods between 1985 and 2010.
Salah Fayed, who died of pancreatic cancer in 2010, was one of three Fayed brothers who purchased the luxury Knightsbridge store in 1985.
Claims of sexual offences by Al Fayed arose in a documentary, after his death, which revealed the extent of his predatory behaviour.
It was only after the broadcast in September that the Metropolitan Police revealed it had been approached by 21 women, before Al Fayed’s death, who accused him of sexual offences including rape, sexual assault and trafficking. Despite this, he was never charged with any offences.
Since the documentary aired, 90 further women have contacted the force, with allegations stretching as far back as 1977. A wider investigation by the Met into the claims against Al Fayed is ongoing.