The United Iraqi Alliance is said to favour the Dawa party leader, Ibrahim al-Jaafari, as the country's next prime minister.
The Shia alliance, which has the support of the Grand Ayatollah Ali al-Sistani, won 48% of the 8,500,000 votes cast in last month's elections in the country.
The other main party in the alliance has agreed to support the candidacy of al-Jaafari and will withdraw its nominee.
The Kurds, who won around 25% of the vote in the 30 January poll, have said they want to nominate a candidate for the largely ceremonial role of president.
They have put forward Jalal Talabani, leader of one of two major Kurdish parties, as their nominee.
