With the opposition giving her two day's ultimatum to step down and hand over power to an unelected "People's Council", Yingluck told a televised press conference that, "I would like everybody to join in finding a solution but I can't find one under the legal framework and the constitution."
Yingluck said the call by anti-government protest leader and former Democrat Party MP Suthep Thaugsuban, to return the ruling mandate and set up a people's council was impossible under the Constitution.
"I will not pose a condition. If I am able to do anything to return peace, I'll be willing to do it but it must done under the provision of the Constitution," she said.
"Please understand me. I don't know which law under the constitution's framework I should invoke to implement the call (of people's council)," Yingluck said.
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"I don't know how to implement Suthep's call under the law. I affirm that I have opened all channels to try to find common solutions. I am open to talks all the time," Yingluck said.
The protesters want to replace the government with an unelected "People's Council", alleging Yingluck's government is controlled by her brother, ousted leader Thaksin Shinawatra.
Thaksin, was ousted in a military coup in 2006 that left the country bitterly divided.
Four people have died and more than 100 injured in the anti-government protests in Thailand's worst political turmoil since the 2010 rallies that ended in violence.