More than 200 women have come forward with allegations since a BBC documentary last week reported claims that Fayed had raped five women who worked at Harrods.
The new allegations include "several" relating to Fayed's time at Fulham, according to a spokesman for the Justice for Harrods Survivors, a group of barristers representing the alleged victims.
The billionaire Egyptian owned the club between 1997 and 2013, during which time he invested about £200m in the team.
A spokesman for Fulham said the club "remain in the process of establishing whether anyone at the club is or has been affected by the reports concerning Mr AI Fayed".
The Football Association said it was "aware of the reports and will remain in contact with Fulham FC to monitor the matter".
During Fayed's time at the club it established its first professional women's team. Gaute Haugenes, who managed Fulham's women's team between 2001 and 2003, told the BBC last week that the allegations had not come as "the biggest surprise".
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