Prince Faisal bin Fahd bin Abdullah says his F6 investment firm is close to buying into Liverpool.
Kop co-owner George Gillett has been in Riyadh this week and held further talks over selling his shares.
Prince Faisal said: "Our negotiations to buy shares in Liverpool are ongoing, meetings are taking place.
"We might be in the final stages in the coming days."
But sources close to Gillett's co-owner, fellow American Tom Hicks, insist they are still a long way off coming to an agreement with the Saudis, says The Sun.
Gillett and Hicks, who took over at Anfield in February 2007, have been seeking new investment at the club since refinancing some of its £290million debt in the summer.