Gaydamak, who has been at the club since January 2006, said late last year that he wanted to sell.
The Franco-Russian initially bought into Pompey as joint owner when he struck a deal with then-chairman Milan Mandaric.
He then bought out Mandaric, who now owns Leicester City, for about £32m.
Under Gaydamak's ownership Portsmouth won the 2008 FA Cup but he says he can "no longer invest the time required to oversee the running of the club".
Since the FA Cup victory, Portsmouth have seen Harry Redknapp depart to manage Tottenham, while his successor Tony Adams lasted just 16 games in charge.
Paul Hart replaced Adams at the helm and guided the club to Premier League safety, but his future at the club is still up for discussion.
Gaydamak had earlier stated that he had rejected two offers for Pompey, as he wanted to sell to a buyer who would be committed to funding a new stadium and training ground for the club.
Al Fahim has previously been linked with an audacious bid for Chelsea.
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