The news came as Iraq's parliament rejected a draft law requiring all foreign troops other than Americans to depart by July.
Britain says its 4,000 troops will withdraw from the southern city of Basra by the end of May.
Army Gen. Ray Odierno, the overall commander of U.S. and allied forces in Iraq, said in an interview with The Associated Press late Saturday that he is considering moving either a brigade or division headquarters - about 100 personnel - as well as an undetermined number of combat troops to Iraq's second-largest city.
Moving a headquarters unit to Basra, the heart of Iraq's vital oil industry, would essentially give the U.S. responsibility there and across the rest of the country for providing training and support to all Iraqi security forces.
"It will be a smaller presence than what is here now. We think it's important to maintain some presence down here just because we think Basra is an important city, and we think it's important to have some oversight here," Odierno told The AP in Basra. The general was briefed there by British Maj. Gen. Andy Salmon about the area's stability and preparations being made to withdraw.
Odierno said Multi-National Division - Center, which is responsible for the area south of Baghdad once known as the "triangle of death" because of violence that was its hallmark, will expand south to the Persian Gulf and the Kuwait border.
After the Dec. 31 expiration of the U.N. mandate authorizing military operations in Iraq, the only coalition troops to remain will be the U.S., Britain, Australia, El Salvador, Estonia and Romania. Britain plans to withdraw its troops by the end of May.
Australia has 1,000 troops in Iraq, followed by Romania with 501, El Salvador with 200 and Estonia with 40.
Iraq's parliament on Saturday rejected for the second time a draft law allowing foreign troops from countries other than the United States to remain until July. If it is not passed before the U.N. mandate expires at the end of the month, those troops will have no legal ground to remain into the new year.
The law, drafted by the government of Prime Minister Nouri al-Maliki, was also rejected earlier in the week. But is expected to be approved in a third and final reading before the end of the year.
Iraq's parliament speaker and his deputies were meeting Sunday with legal advisers and British embassy officials to reach a solution allowing the draft law to be approved, lawmaker Ridha Jwad Taqi of the Shiite United Alliance told the AP.
A separate agreement approved by the Iraqi government on Dec. 4 allows the United States to keep troops in the country until the end of 2011. That agreement, which takes effect on Jan. 1, gives Iraq strict oversight over the nearly 150,000 American troops now in the country.
Odierno has said that even after that summer deadline, some U.S. training teams will remain in Iraqi cities.
He also said no decision has been made to withdraw the nearly 22,000 Marines in Iraq, mostly in Anbar province, where insurgent violence is relatively low, despite comments from the Marine commandant that there was a greater role for his troops in Afghanistan.
"We will take into account what is going on in Anbar, in the rest of the country, to make sure that we have the proper force structure to continue our mission to make sure we don't give up any of the security gains we have," he said.
Chief among Odierno's concerns about maintaining stability in Iraq is providing adequate security for the Jan. 31 Iraq-wide provincial elections.
He will make a decision about the future duties of American troops about 60 days after January's provincial elections, enough of a period of time to monitor and deal with any violence that might arise.
"So we have to make sure in the election those who didn't win understand that, and we will be able to seat the new government properly," Odierno told The AP late Saturday. "And once we get to that point, it's now time for us to take a look at what is right for the future."
Meanwhile, in violence Saturday, an Iraqi officer was killed when gunmen fired on a police patrol in the restive northern city of Mosul.
The shooting took place Saturday at the Al-Sha'areen market in the center of Mosul, a police officer said on condition of anonymity because he was not authorized to speak with news media.
The officer also said a roadside bomb wounded two members of an Iraqi army patrol in the city on Saturday.