JOIN USMedia reports here said that a recommendation in this regard has been sent to the White House by the Defence Secretary Leon Panetta.
But the White House and Pentagon denied the reports and said the option would be considered only if Iraq made such a request.
"We have said in the past that, if the security component of that relationship, if the Iraqi government makes a request of us, we will certainly consider it. That request has not been made, no decisions have been made, and so we are operating, as of now, under the existing agreements," the White House Press Secretary Jay Carney said.
The President, he said, has made abundantly clear for a long time now that he will end US efforts in Iraq responsibly.
"We have been operating on a timetable that has withdrawn over a hundred thousand US forces since he took office, in a way that has been incredibly careful and responsible and has allowed the Iraqis to further build up their security forces and improve their capacities," Carney said.
"What our relationship looks like going forward with Iraq will depend upon our negotiations with the Iraqi government," he said.
"Discussions with the Iraqis on our post-2011 strategic relationship are on-going, and no decisions on troop levels have been made. We continue to proceed with troop withdrawals as directed by the President," said the Pentagon spokesman George Little.
However, CNN said despite adamant statements that no final decisions have been made about future US troop levels in Iraq, discussions within the administration have included a potential option for keeping just 3,000 forces there beginning next year.
There are currently more than 40,000 US troops in Iraq. The current agreement is for all troops to withdraw by year's end.
However, the US expects the Iraqis to request some US troops to remain to aid in training and security, it said.
According to The New York Times, the proposal for a smaller force — if approved by the White House and the Iraqi government, which is not yet certain — reflected the shifting political realities in both countries.
"It also reflected the tension between Mr Obama's promise to bring all American forces home and the widely held view among commanders that Iraq is not yet able to provide for its own security.
"And it reflected the mounting pressures to reduce the costs of fighting in Iraq and Afghanistan, both wars that have become increasingly unpopular as the 10th anniversary of the attacks of Sept 11, 2001, approaches," the daily said.Three top Senators came out openly against the plan.
"We are deeply troubled by media reports that the Obama Administration has sharply reduced the number of US troops it is proposing for the post-2011 security force in Iraq to approximately 3,000," said a joint statement issued by Senators John McCain, Joe Lieberman and Lindsey Graham.
"This is dramatically lower than what our military leaders have consistently told us over the course of repeated visits to Iraq that they require, and that is needed to support Iraq in safeguarding the hard-won gains that our two nations have achieved at such great cost," they said.