Under an agreement with the Taliban, the US must leave by 31 August.
But France, the UK and Germany all raised the possibility of allowing more time ahead of a summit on Tuesday.
US President Joe Biden is set to decide within the next 24 hours whether to extend the timeline for withdrawal, an official told Reuters news agency.
However the Taliban have told the BBC that any extension would violate the agreed deal and warned of consequences if forces remained.
Tens of thousands of people have been evacuated from the Afghan capital Kabul, but others seeking to flee remain crammed in or near the city’s airport, which is guarded by US forces and their allies.
Many of the people fleeing, particularly those who worked with foreign forces, live in fear of reprisals from a group that imposed a harsh version of Islamic law when in power from 1996 to 2001.
France’s Foreign Minister Jean-Yves Le Drian told reporters in the UAE: “We are concerned about the deadline set by the United States on August 31. Additional time is needed to complete ongoing operations.”
Germany’s Foreign Minister Heiko Maas said he had discussed keeping Kabul airport open beyond the deadline with Nato allies and the Taliban.
On Tuesday, UK Prime Minister Boris Johnson is expected to push the US for an extension during the virtual summit with other G7 leaders. Defence Secretary Ben Wallace said the prime minister was “going to try and raise the prospect of seeing if the United States will extend” its withdrawal.
The UK has said that any foreign military presence at Kabul airport cannot continue without US troops.
Military advisers have told the White House that a decision needs to be made on Tuesday in order to allow for the troops along with their equipment and weapons to leave in time for the deadline, CNN reports.
A defence official told the network that if Mr Biden agreed on withdrawing in time for the deadline, there would be “a few more” days of evacuating people before the drawdown of troops began, possibly at the end of this week. Currently 5,800 troops are on the ground.
According to the White House, about 10,900 people were evacuated from Kabul between 11:30 and 23:30 local time (07:00 – 19:00 GMT) on Monday.
The US has evacuated, and facilitated the evacuation of, approximately 48,000 people since an intense airlift started on 14 August, the White House said.
Images from Washington’s Dulles Airport shows Afghans arriving in the country.
The Taliban has tried to paint a conciliatory picture for those Afghans who stay, asking them to help rebuild the country. Taliban spokesman Suhail Shaheen told the BBC people with passports would still be able to leave on commercial flights after the deadline.
He said: “We want them to stay in the country but if they intend to go, they can.”
The airlift began as the Taliban moved into Kabul following a lightning campaign that saw them take over almost all of the country in the wake of the US decision to withdraw forces.
The sole remaining area holding out appears to be the Panjshir region north-east of Kabul, a stronghold of anti-Taliban opponents who say thousands of people are ready to carry on the fight.
The Taliban were ousted by US and allied troops following al-Qaeda’s 11 September 2001 attacks. A 20-year conflict ensued. (Courtesy BBC)