A possible replacement for Mr Papandreou is currently being discussed, the sources have also indicated.
The development comes after the country's opposition leader insisted the PM must go to save the economy.
Antonis Samaras said he was willing to help in the formation of a coalition government - but not until Mr Papandreou had stepped down.
Despite winning a confidence vote in parliament, Mr Papandreou has struggled to form a temporary coalition government to back the controversial EU bailout package.
The prime minister had gone into talks with president Karolos Papoulias on how to construct an administration to negotiate the deal to write down Greek debt and release billions in emergency aid.
But sources within Pasok - the socialist party that Mr Papandreou heads - have told Sky News there are only two possible scenarios.
The first involves Mr Papandreou stepping down and being replaced by a compromise candidate who is acceptable to both the left and right of the political spectrum.
The second scenario would see Mr Papandreou stepping down and being replaced by someone within Pasok itself - potentially Evangelos Venizelos, the current finance minister, who has been part of the bailout negotiations.
An emergency cabinet meeting will be held this afternoon, when these issues will be discussed.
The country is under pressure from the eurozone's power brokers to implement the bailout package agreed in Brussels on October 27.
If the bailout stalls in the Greek parliament, that would hamper the release of money Greece needs to pay salaries, pensions and international creditors.
After the prime minister won a confidence vote in the early hours of Saturday morning, European finance ministers, who meet next week, will want to see progress in Athens.
However the opposition New Democracy party is angry Mr Papandreou decided to tough out his tenure, rather than call snap elections.
Its (Euronext: ALITS.NX - news) leader, Mr Samaras, said the prime minister was "dangerous" for Greece.
But he and other opposition leaders have already said they would work to implement the bailout deal, so the pressure to join a consensus government is immense.
Greece's shadow finance minister Notis Mitatarakis told Sky News he believes the leader of the country's new interim government did not have to be a politician.
"We need elections because we need a stable government to be able to negotiate the new loan agreement," he said.
"However, we realise the need for an interim government in order to conclude the loan agreement [and] the restructuring of the Greek debt.
"That would need a person that is mutually accepted, not necessarily a politician - rather, not a politician - to run an interim government and then go to elections."
The wrangling comes after almost a week of market anxiety over whether the near-bankrupt country will actually embrace the bailout deal.
Mr Papandreou has already abandoned a proposal to hold a referendum on the package, which would result in years of financial austerity for Greece.
On Friday world leaders drew a blank in their efforts to resolve the wider eurozone crisis, as a G20 summit ended with no agreement on crucial measures to shore up ailing economies.
The Group of 20 leading economies failed to thrash out a detailed plan to stabilise the single currency or to boost the International Monetary Fund's ability to respond to emergencies.
Prime Minister David Cameron warned squabbling eurozone leaders "the world can't wait" for them to finalise plans to bailout Greece, recapitalise banks and erect a one trillion euro (£870bn) "firewall" to protect the single currency.
He acknowledged that the ongoing uncertainty in the eurozone was having a "chilling" effect on the British economy.