Al-Fahim will sell the stake to a consortium led by Saudi Arabian property tycoon Ali al-Faraj.
Al-Fahim told The Observer: “I think by Monday or Tuesday (Al-Faraj) will be on the board. His consortium will be a major shareholder. And I will keep a minority.”
Portsmouth chief executive Peter Storrie told the Sunday Mirror: “It was imperative that something had to be done to safeguard the future of this club.
“Portsmouth were completely skint and when it appeared funding from Sulaiman Al-Fahim wouldn’t arrive in time to stop the club from being put into a perilous situation we had to do something.
“After prolonged talks with Ali-Al-Faraj we eventually came to a solution and subject to all the legal issues being sorted out, I am confident the deal should go through early next week.”
Al-Fahim only completed his takeover of Pompey in late August.