Negotiations over the 4.6 billion baht ($113 million) bid for a 30 percent stake in the club are believed to have stalled over the level of Thai representation on the Liverpool board.
"There definitely won't be any signing this Friday, Saturday or Sunday," Thaksin said in response to media reports that the deal could be completed this weekend.
"But we are trying to wrap up the deal next week because we don't want to see it drag on," the telecoms-tycoon turned politician told reporters.
The Thais want two seats on the Liverpool board while the club are offering only one, Thai newspapers reported.
Liverpool are 51 percent owned by chairman David Moores, whose family has had control for half a century, and 9.9 percent owned by television company Granada.
Thaksin has said Moores' holding would drop to around 35 percent if the deal went ahead.
"The pending issue in the talks involves the question of minority protection. We don't hold the majority. 30 percent is a minority and there should be reasonable protection. It is not a small amount of money," Thaksin said.
'WE WAIT'
Liverpool officials have said the talks are ongoing, but refuse to comment further.
Deputy Commerce Minister Pongsak Raktapongpisal, the chief Thai negotiator, said 80 to 90 percent of the details had been worked out, but the shareholder rights issue was still pending.
The Thais, who said earlier this week they had an agreement in principle with Liverpool, are waiting for the club's response to their latest amendments.
"Now we wait. In any business deal, the first step is the signing of the MOU (memorandum of understanding). If further negotiations cannot be concluded, the deal may be off," Pongsak told Reuters.
Thaksin has said the Thai offer would inject 45 million pounds ($80.7 million) into the club, which needs investment to buy players and help fund the construction of a bigger stadium.
The rest will go to buy shares from existing shareholders.
The billionaire prime minister was initially expected to put up some of his own money. He ran into fierce opposition when officials suggested government funds would be used.
Thaksin now wants to set up a company to manage the investment, and raise funds to finance the purchase through a one-off state lottery.
Critics say the money will be wasted and they doubt Thaksin's claim that the deal will benefit Thai soccer by setting up a Liverpool academy in the southeast Asian country.
