The Shias will take 16 to 17 ministries in the next government, the Kurds will hold seven to eight ministries, and the country's Sunni minority will be awarded four to six ministries, Shia negotiator Mariam Rais said.
Kurdish sources confirmed the numbers, while both sides predicted that an agreement on the government should be reached before Sunday.
The Shias will take the interior and finance ministries, along with the cabinet post of national security adviser, according to Rais, a negotiator with the United Iraqi Alliance (UIA) that won 146 seats in the new 275-member parliament.
With 77 seats the Kurds - the second largest block in parliament - will receive seven to eight ministries, including the foreign ministry and probably oil, Rais said.
A Kurdish source also confirmed the Kurds were likely to get eight ministries, including oil and foreign affairs.
The source said other posts that were locked up included the presidency, to be held by Jalal Talabani, and the post of deputy prime minister.
The secular list of Iyad Allawi (R)
has not been allotted any slots
One complication that could change the allotment of slots is whether outgoing interim prime minister Iyad Allawi's secular list decides to join the government, which remains unclear, the Kurdish source said.
Rais further said Iraq's Sunni division would probably be awarded between four and six posts, while the Christian and Turkmen minorities would receive one ministry each.
Rais said she thought it was doubtful Allawi or his followers would join the government.
Al-Mutamar, the newspaper of secular Shia politician Ahmad Chalabi, said outgoing secular Sunni President Ghazi al-Yawar would be the parliament's new speaker and fellow secular Sunni politician Hajim al-Hasani would serve as vice president.
Separately, UIA spokesman Haitham al-Husaini said the sides were hoping to convene the second session of parliament on Thursday after a first session last Wednesday.
"There's the proposal for the parliament to meet this coming Thursday. It's a great possibility, but its not confirmed yet. It's all under discussion, the other possible date is Saturday."
The Kurdish source said the parliament should convene by Sunday at the latest.
Against this backdrop of political horse-trading, four Iraqis were killed and a number of US soldiers injured on Tuesday in an explosion caused by an explosive device, planted on Sinharib bridge in central Mosul city, Aljazeera reported.
A US Humvee was also damaged in the explosion.
The area has been cordoned off by US forces, with military vehicles heavily deployed in the area.
But an Iraqi deputy police commander, Colonel Wathiq Ali, gave a conflicting account of the incident, saying a gun battle in front of a mosque had led to the death of 17 fighters and the detention of 14 more.
"There's the proposal for the parliament to meet this coming Thursday. It's a great possibility, but its not confirmed yet. It's all under discussion, the other possible date is Saturday"
Ali also said no security forces were injured in the clash, in which mortar launchers, rocket-propelled grenades and Kalashnikov rifles were used.
Also on Tuesday, morgue officials in southern Kut said they had received a half-dozen corpses of Iraqi army soldiers with bound hands and bullet-riddled heads and torsos.
Each of the soldiers had their hands tied behind their backs, with multiple gunshot wounds to the head and chest, according to Hadi Al-Itabi, head of the morgue at Al-Zahraa Hospital in Kut, 160 km southeast of Baghdad.
Iraq Defence Ministry officials said they had no information on the incident.
Overnight, three rockets landed on the town of Iskandaria, south of Baghdad, killing one child, according to a local police official who asked not to be named for security reasons.
Violence across Iraq rages while
politicians seek a settlement
Gun battles broke out on Tuesday in the streets of the southern Baghdad neighbourhood of al-Dura.
Shopkeepers and residents say they returned fire after a car reportedly carrying three hooded men opened fire on shoppers.
The three hooded men were reportedly killed in the shootout. A man, woman and child were among the injured and were taken to a local hospital.
In the eastern city of Kirkuk, the director of the Iraqi army's legal department died on Tuesday of wounds suffered late on Sunday when armed men shot him outside his home, General Anwar Muhammad Amin of the Iraqi army said.
The US military reported the death of a marine in the western Anbar province.
The marine, assigned to the 1st Marine Expeditionary Force, was killed in action on Monday in Anbar province which includes the cities of Fallujah and Ramadi, the US military said in a statement.
No further details were given. The marine's name was being withheld pending notification of next of kin.