According to the Associated Press, a spokesman said on Tuesday that al-Jafari went into a meeting with President Jalal Talabani and that, if the list is approved by the three-member presidential council, the prime minister will submit it to parliament for a vote, possibly on Tuesday.
Al-Jafari's spokesman, Abd al-Razzaq al-Qadi, said the party of outgoing Prime Minister Iyad Allawi was not included.
Al-Qadi provided no details of the cabinet proposal. But lawmakers from al-Jafari's Shia-dominated United Iraqi Alliance said it included 31 ministries, spread between Shia, Kurds and Sunnis.
Iraqi politicians have been under US pressure to form a new transitional government nearly three months after 30 January elections.
Many in Iraq believe the impasse has emboldened fighters, who have launched well-coordinated attacks on US troops and Iraqi security forces in recent weeks, causing many casualties.