FSG have opened talks with groups from Saudi Arabia and Qatar about selling Liverpool.
The Daily Mail says they have held discussions with two Middle East-based consortiums over a £3billion takeover.
Representatives of consortiums from Saudi Arabia and Qatar have expressed an interest in buying the club.
Several sources report that consortium officials have approached Fenway Sports Group director Mike Gordon - the man responsible for the sale of Liverpool - to register their interest.
It is understood both groups are private companies rather than state-owned.
However both consortiums are thought to have close links with their country's ruling families.
Both clubs have been exploring potential sales options over the past month.