"I think we will be in need of American forces for a long time -- even two military bases to prevent foreign interference," Mr Talabani told The Washington Post.
"I don't ask to have 100,000 American soldiers -- 10,000 soldiers and two air bases would be enough."
The president indicated the bases would most welcome in Kurdistan, an autonomous region in northern Iraq that has practiced de facto self-government since the 1991 Gulf War.
But he suggested that the Sunni Arab segment of the Iraqi population would also welcome a long-term US military presence in Iraq.
"In some places Sunnis want the Americans to stay," he said. "Sunnis think the main danger is coming from Iran now."
Mr Talabani’s comments come as top US military commanders admit that the United States will not be able to reduce its 147,000-strong contingent in Iraq because of spreading sectarian violence and the possibility of the country slipping into civil war.
US Central Command head General John Abizaid has said that any previous plans to draw down US troops in Iraq had been put off until at least next spring, and warned the force level might even go up.