Iraq's largest parliamentary bloc, the United Iraq Alliance (UIA), is to vote on a candidate for prime minister.
Iraq's parliament is due to meet again on Saturday
The Shia coalition's previous choice, interim Prime Minister Ibrahim Jaafari, has reportedly rescinded his nomination amid Sunni and secular opposition.
Disagreement over the new prime minister has held up the formation of a new government, months after elections.
But correspondents say the lack of a credible alternative candidate could lead to fresh political turmoil.
At least two potential candidates are believed to be in the running - Ali al-Adeeb and Jawad al-Maliki - both members of Mr Jaafari's al-Daawa party.
But the BBC's Jim Muir in Baghdad says neither is particularly well-known and the appointment of either could, once again, run into trouble with the Kurdish, Sunni and secular factions, whose support is needed for the formation of a national unity government.
Change of heart
The UIA is expected to announce a leader by Saturday afternoon when the parliament is due to hold a session, which was postponed from Thursday.
Saturday's session, at which MPs are due to choose a speaker, likely to be drawn from the Sunni Arab parliamentary contingent, will be only its second since the general election in December.
Wrangling between Sunni, Shia and Kurdish parties over who should be prime minister has prevented the formation of a government.
Mr Jaafari narrowly won the PM nomination in February
As recently as Wednesday, Mr Jaafari was refusing to step aside, insisting his nomination was the democratic choice of the Iraqi people.
A meeting with United Nations envoy Ashraf Qazi and Shia Muslim religious leaders were key factors in Mr Jaafari's change of heart, correspondents quote MPs as saying.
As Shia political leaders tried to resolve the impasse, violence continued across the country.
In the latest incidents:
- A baker heading to work in Baghdad is shot in a drive-by shooting and the bullet-ridden bodies of two other Iraqis are found in the capital, reports quoting police say
- A roadside bomb aimed at a US military patrol explodes in Dora, missing its target but wounding two Iraqi civilians, reports say
- On Thursday, at least nine people were killed in scattered violence in Iraq.
The UIA emerged as Iraq's largest political group following parliamentary elections on 15 December 2005, with 128 out of 275 seats.
Our correspondent says that there is no obvious candidate of stature waiting to replace Mr Jaafari.
In February he won a similar internal nomination poll by just one vote, beating Vice-President Adel Abdel Mahdi.
The US and UK have been putting pressure on Iraq's political factions to set up a unity administration - something all sides agree is needed to end the instability and unrest gripping Iraq since the US-led invasion in 2003.