But his arrival was said to have had an unsettling influence on the players, with talk of a power struggle between the Italian and manager Jean Tigana.
The Fulham manager was reportedly furious that Baresi, who was offered an initial six-month deal, would assume overall responsibilty for all football matters at the club.
Baresi's position was then scrapped, as were his demands for a three-year contract, and he worked without a job title while living in one of Al Fayed's luxury central London penthouses.
"I have decided that it would be in my own professional interests, and also a sensible outcome for Fulham, to terminate our brief relationship," Baresi told the club's official website.
"While all parties have worked constructively to develop our respective roles, I am disappointed that the nature of my position with Fulham was not as I had envisaged it when I was first approached.
"It makes sense to recognise this sooner rather than later, and particularly before I make commitments which involve not only myself but also my family."