They have rejected his offer to hold a referendum asking the public to decide whether he should stay or go.
The impasse stems from a campaign by the People's Alliance for Democracy (PAD) - a loose-knit group of royalists, wealthy and middle-class urban residents, and union activists - to oust Samak and his government, accusing it of corruption and of violating the constitution.
Finding a quick replacement for Tej is crucial for Bangkok, currently holder of the rotating chairmanship of the 10-member Association of South East Asian Nations (Asean) and host of its regional summit in December.
Saroj retired as ambassador to France in 2001 and has served as the head of various departments in the foreign ministry.
Samak, meanhwile, has refused to negotiate with the protesters, telling reporters on Friday: "No, that won't be necessary."
But he has accepted a new proposal by parliament to let Prasopsuk Boondet, the senate speaker, act as a mediator.
The decision to attempt mediation was made by the opposition Democrat Party and leaders of the two chambers of parliament - the senate and house of representatives.
Abhisit Vejjajiva, the Democrat leader, told reporters on Saturday: "The speaker has agreed to find a way to get the two sides to sit down and talk to find a way out."
PAD leaders rejected a proposed referendum, with analysts saying it would be a futile exercise and could divide the country.
Critics opposed the idea, arguing that the balloting would only drag out the turmoil and risked sparking new unrest.
They cited clashes among rival protesters that left one of Samak's supporters dead early on Tuesday.
Abhisit also said on the website for the Thairath newspaper that the referendum would not resolve the stalemate.
He proposed that Samak dissolve parliament and call snap elections.
"The referendum is going to be a non-starter," Thitinan Pongsudhirak, a political analyst at Chulalongkorn University, said.
"We're back to the same confrontation."
After the deadly violence on Tuesday, Samak declared a state of emergency in Bangkok, the capital, essentially handing control of the city to General Anupong Paojinda, the head of the army.
Anupong has so far refused to evict the squatters who have turned their camp on the Government House lawn into a small village.
Protesters there receive free food and even complementary haircuts.
Thais are deeply divided by the protests, with one survey of 16 provinces showed that 50 per cent of respondents supported the movement.
The finding highlights the social divide that has ripped Thailand apart in recent years, with Bangkok's traditional elite backing the PAD while poor but populous rural areas support Samak.
Thaksin Shinawatra, a former prime minister, was the first politician to rally Thailand's rural voters with low-cost loans and free healthcare.
But the PAD staged mass protests against Thaksin in 2006, accusing him of corruption and paving the way for a military coup in September 2006.
Thaksin has fled to Britain to escape corruption charges, but he backed Samak to lead his supporters to victory in elections last December, ending more than a year of military rule.