The White House has said for the first time it is possible that no US troops will remain in Afghanistan past 2014, as President Hamid Karzai arrived in Washington for talks with Barack Obama.
Ben Rhodes, a top US security official, told reporters the administration was still considering a range of options.
Mr Karzai's three-day trip will include crucial talks with Mr Obama and other officials, but no final decision.
The Afghan president wants US troops out of Afghan towns and villages.
Correspondents says the meeting comes as relations between the two countries have been more fractious than usual.
When asked whether the US was considering a "zero option" for a residual force after the end of the US combat mission in 2014, Mr Rhodes, the deputy national security adviser, told reporters: "That would be an option that we would consider."
"The President does not view these negotiations as having a goal of keeping US troops in Afghanistan," Mr Rhodes said, adding the US' position would be guided by the "two goals of denying a safe haven to al-Qaeda and training and equipping Afghan National Security Forces".
Most foreign combat troops, including Americans, will leave Afghanistan by the end of 2014. There are currently about 68,000 US soldiers in the country.
Mr Rhodes told reporters that an announcement on post-2014 troop levels was not expected during Mr Karzai's visit.
But he added that a bilateral security agreement between the US and Afghanistan is expected by November of this year.
White House officials have previously suggested they favour keeping between 3,000 and 9,000 troops in Afghanistan after the combat mission ends.
The Afghan leader is due to see President Obama on Friday, their first meeting since the US presidential election.
Ahead of the trip, the White House issued a statement saying Mr Obama "looks forward to... discussing our continued transition in Afghanistan, and our shared vision of an enduring partnership" between the two countries.
The BBC's Quentin Sommerville in Kabul says the US president is likely to discuss the size of the force that remains, and whether they are there to fight the Taliban or shift their primary focus to tackling al-Qaeda.
The visit comes days after a drone attack that killed Pakistan militant leader Mullah Nazir, who was accused of sending fighters to Afghanistan to support the Taliban.
Mr Karzai is expected to provide a request for future requirements for the Afghan military such as heavy weaponry, an improved air force and medical support.
Our correspondent says the US spent almost $120bn (£74bn; 91bn Euros) in Afghanistan in 2011, a figure that diplomats in Kabul say will be increasingly difficult to justify because of economic problems at home and extensive corruption within Afghanistan.
Meanwhile Mr Karzai has held back from signing a long-term binding security agreement with the US, amid fears that Afghan sovereignty is being undermined.
He is unwilling to grant US soldiers immunity from prosecution and is unhappy that Afghans are still being held in US-run military prisons on Afghan soil, our correspondent adds.
US and Iraqi authorities reached a similar sticking point in negotiations over the drawdown of US troops from Iraq. Aside from a contingent guarding the embassy, all US soldiers left the country by December 2011.
As of December, Nato forces in Afghanistan numbered 102,000, including 68,000 US troops.