The ban would prohibit troops from Ethiopia, Djibouti and Kenya from being part of the peacekeeping mission.
But Uganda, which is the only country thus far to volunteer troops to the regional group, the Intergovernmental Authority on Development, known as IGAD, will be allowed to take part.
John Bolton, the US ambassador to the UN, said he expected the draft to be discussed on Monday "and then we'll proceed as rapidly as we can after that".
The new regional force would protect the transitional government, based in Baidoa, and train some of the local forces.
Diplomats said the IGAD envisions a force of eight battalions, each with 700 to 800 troops, but only two would be deployed in the first phase.
"What we want to do is introduce this regional peacekeeping force ... which many of the African states have called for, in order to provide some measure of stability there to permit a political solution"
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"It's very limited," Emyr Jones Parry, Britain's ambasador to the UN, said. "The situation in Somalia ... remains very difficult and complex, and there isn't a simple solution, and there certainly isn't a massive imposed military solution from outside."
Somalia has been without an effective government since Mohamed Siad Barre in 1991. The government was formed with the help of the UN two years ago, but has struggled to assert its authority.
The Union of Islamic Courts, which opposes the government, has taken control of the capital, Mogadishu, and most of the country's south.
Bolton said the transitional government "is under pressure from the Islamic Courts Union movement" and Somalia's stability "is in grave peril."
"What we want to do is introduce this regional peacekeeping force ... which many of the African states have called for, in order to provide some measure of stability there to permit a political solution," he said.
A UN report has said that 6,000-8,000 Ethiopian troops are in Somalia or along the border, supporting the transitional government. It also said 2,000 soldiers from Eritrea were inside Somalia, supporting the Islamic courts.
There are fears that Somalia could become a proxy battleground for Ethiopia and Eritrea.
The draft emphasises the council's "willingness to engage with all parties in Somalia, including the Union of Islamic Courts, if they are committed to achieving a political settlement through peaceful and inclusive dialogue."
A report earlier this month accused 10 countries of providing weapons, money and training to rival sides in Somalia. Many of those named have denied any involvement and complained about being on the list.