Paiboon Damrongchaitham, chairman of Thai music publisher GMM Grammy and close friend of Shinawatra, heads the consortium hoping to buy a 30% stake in the club.
Such a deal is likely to include shirt sponsorship, a football academy and summer tours to South East Asia.
Damrongchaitham expects to hear whether the latest bid is successful by the end of the month and, if it is, should go through by the end of the year.
"We have sent out proposal about rights and benefits to Liverpool and expect an answer from them on whether there will be another discussion or not," he said.
"The price will be the same as the Thai government proposed, but the number of shares may be less or more.
"After the purchase I will list shares of Liverpool Thai Holding on the Thai stock market."