US President Barack Obama is considering the option of leaving no troops in Afghanistan after the scheduled pullout date of December 2014.
The White House is preparing to receive Afghanistan's President Hamid Karzai to co-ordinate future security plans.
It says one of the options being considered is to have a total withdrawl of the remaining 66,000 American troops by the end of next year.
US Defence Secretary Leon Panetta favours keeping 9000 troops in order to continue training Afghan forces and maintaining the ability to fight al Qaeda in 2015 and beyond, Radio New Zealand's correspondent in Washington reports.
Mr Karzai will be discussing the issue during the meeting with Mr Obama as the leaders work towards a new bilateral security agreement.
Meanwhile, the Nato-led international force in Afghanistan says it will transfer to Afghan forces the lead role in ensuring security in 12 more of the country's 34 provinces in February.
Afghan forces will then have primary responsibility for security in two-thirds of the provinces.