The caretaker prime minister made her call during meeting on Wednesday with Gen Prayuth which sparked wide speculation and reportedly upset PDRC secretary-general Suthep Thaugsuban.
Ms Yingluck abruptly cancelled her trip to Khon Kaen and met the army chief at the Royal Thai Air Force headquarters.
The source said the caretaker prime minister is hoping to negotiate with Mr Suthep and wants Gen Prayuth to mediate. She prefers the talks to be held behind closed doors, not in public as proposed by Mr Suthep.
The caretaker prime minister said the talks are aimed at seeking popular support rather than trying to resolve political differences and end the stalemate.
Gen Prayuth told Ms Yingluck that he has made several attempts to convince Mr Suthep to hold talks but the protest leader does not want them to be held in private, the source said.
Last year, Ms Yingluck and Mr Suthep met in the presence of military leaders and the meeting ended without any resolution.
Ms Yingluck recently called on the protest leader to go to the negotiating table. Mr Suthep scoffed at that and told her to join him in a public debate to be broadcast live on television.
The source said Gen Prayuth informed the caretaker prime minister of the mid-year military reshuffle in which some senior military officers involved in the 2010 military crackdown would be promoted to key posts.
Gen Prayuth was concerned these officers would come under attack from the red shirts for their role in that military operation and their promotion might irk the red shirts, the source said.
The army chief hoped the prime minister would help the red shirts understand the officers acted under orders and that none held personal grudges against the red-shirt demonstrators.
The source said the caretaker prime minister promised to talk to the red-shirt leaders and said she would not interfere in the military reshuffle.
The source said among those to be promoted in the mid-year reshuffle is 1st Army Corps commander Lt Gen Walit Rojanapakdi.
Lt Gen Walit was in charge of crowd dispersal during the red-shirt protests in 2009 and 2010. He was commander of the 2nd Infantry Division and was assigned to clear red shirts from Din Daeng intersection in Bangkok on April 12 and 13, 2009.
The following year, on April 10, 2010, he led his unit to disperse red-shirt protesters at Kok Wua intersection during clashes between demonstrators and security forces. He was seriously injured when grenades exploded during the clashes.
Ms Yingluck said yesterday the Wednesday talks were held to "address concerns" of both the government and the military. But she stressed it was not about the alleged secession issue.
"There is nothing to clear up about that. We have made it clear we will protect the country. I insist there is no separatism. Thailand is whole and undivided," she said.
"They [Sor Por Por Lanna] are asking us to stop talking about this. The more we talk about it the more divided we become."
Some people believe Sor Por Por Lanna stands for the Lanna People's Democratic Republic. However, the premier was referring to the Assembly for the Defence of Democracy, a network of academics in the North, which has the same acronym.
The meeting between Ms Yingluck and Gen Prayuth came amid tensions over the northern separatist issue. The army chief has ordered the 3rd Army, in charge of the North, to file a lawsuit against red-shirt network leaders in Chiang Mai for alleged separatism after cloth banners sprung up in northern provinces which were interpreted by some as campaigning for a separate state.
A source close to the PDRC said the PDRC leader is "upset" with Gen Prayuth's role. Instead of pressuring the prime minister to step down, Mr Suthep complained the army chief allowed Ms Yingluck, as defence minister, to discuss the military reshuffle.
Mr Suthep has so far made friendly gestures to the military when he has asked the military to stop supporting the Yingluck administration.
"Everyone [PDRC core members] are upset that Gen Prayuth let Ms Yingluck chair the Defence Council meeting and talk about the reshuffle, when she has no legitimacy nor power to do so," the source said.
The source said Mr Suthep will not negotiate with Ms Yingluck because it will only serve the prime minister's interests. The PDRC secretary-general sees the proposed talks as nothing but an attempt to prolong her stay in power.
Ms Yingluck chaired the Defence Council meeting on Tuesday at the Royal Thai Air Force headquarters which Gen Prayuth and other military top brass in attendance.
The source said Gen Prayuth may now come under heavy criticism by the PDRC.
"He doesn't do anything. He simply leaves it to the court and independent agencies. It could be too late," the source said.
Centre for Maintaining Peace and Order (CMPO) chief Chalerm Yubamrung yesterday changed tack, saying he will speak personally with Mr Suthep.
In a press interview, Mr Chalerm said he changed his standpoint because he wants peace in the country.
He said he wants to meet Mr Suthep at his home in the Phutthamonthon area but that talks cannot happen if there is a condition Ms Yingluck must resign first.
"Would you convey my message to the kamnan (Suthep) that I would like to meet him at his home. I will go there alone, but I will not go if there is a condition the premier must first quit," Mr Chalerm said.
He said it was his own idea and that he did not need permission from the caretaker prime minister nor from former premier Thaksin Shinawatra.
Mr Chalerm said he wanted Mr Suthep to allow the election to be completed so a new administration could be set up. After that Mr Suthep could propose his reform blueprint to the government.
Wutthisarn Tanchai, of the King Prajadhipok's Institute, on Thursday voiced support for closed-doors talks. If they were not private he said there was a chance they would fail. The academic said both sides need to build mutual trust for talks to proceed and accept each other's flaws and strengths.
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