The commander of the NATO-led International Security Assistance Force (ISAF) in Afghanistan, General Joseph Dunford, presented the option last week to the White House, which is weighing the proposal, the official said, confirming reports in the Wall Street Journal and the New York Times.
"It's fair to say that the intelligence community, the State Department, the Pentagon, all believe that if we're going to have a footprint in Afghanistan after 2014, it should be about that number," said the official, referring to the 10,000 troop level.
The option being debated by the White House also calls for a short stay for the proposed post-2014 force, which would be scaled back and withdrawn within two years, the official said.
Such a scenario would allow Obama to tout the end of the longest US war by the time he leaves office in January 2017. But the move could prompt accusations of an irresponsible retreat after repeated vows by Washington to maintain an enduring presence in Afghanistan.
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Under the Pentagon proposal, US commanders hope the 10,000 US troops would be joined by 2,000-3,000 forces from other NATO countries, according to the Wall Street Journal.
Military commanders have reportedly told the White House that if Obama rejects the 10,000 troop option, then all American forces should be withdrawn as a smaller force would be unable to provide security for intelligence officers and diplomats.