"I think we will be in need of American forces for a long time - even two military bases to prevent foreign interference," Talabani told The Washington Post in an interview published on Monday.
"I don't ask to have 100,000 American soldiers - 10,000 soldiers and two air bases would be enough."
The president indicated that the bases would be most welcome in Kurdistan, an autonomous region in northern Iraq that has practised 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 argued. "Sunnis think the main danger is coming from Iran now."
The comments come as top US military commanders admitted that the US would not be able to reduce its 147,000-strong contingent in Iraq in the coming months because of spreading sectarian violence and the possibility of the country slipping into civil war.
General John Abizaid, US Central Command head, said last week that any previous plans to draw down US troops in Iraq had been put off until at least next spring, and the force level might even go up.
"I think these are prudent force levels," Abizaid said of the current contingent.
"We'll bring in more forces if we have to."