FSG are prepared to sell a stake in Liverpool.
Liverpool owner John W Henry announced last month that the club would not be sold outright, four months after the first story broke that they were considering a sale.
Henry said the ambition is to find a third party who could add to their investment.
Major media companies are been examined by FSG as possible investors, The Telegraph says.
US media giant Liberty Media has reportedly emerged as a contender to invest.
Liberty Media are best known for their ownership of Formula One, having taken control from Bernie Ecclestone at the end of 2017 in a deal worth £6billion.
The company also owns the Atlanta Braves baseball team and SiriusXM Group, with their overall net worth estimated at £17.5billion by Forbes.
