The company in question, GMM Grammy, are thought to have already made contact with the Liverpool hierarchy in the hope of meeting with the club to discuss the bid of the private consortium next week.
Shinawatra's decision to bow out will placate the Thailand public, while Grammy's interest will maintain a Thailand interest in the affairs of Anfield.
Deputy commerce minister Pongsak Ruktapongpisal, the government's chief negotiator for the proposed bid, said: "The prime minister is giving up the idea to buy the Liverpool stake under the name of Thailand after the private sector offered to do it in the name of a consortium."