All U-S troops could be out of Afghanistan by the end of next year.
According to White House officials - the administration was considering leaving up to 15,000 troops behind to fight insurgents and train Afghan security forces.
But now the president is said to be "open" to a scenario that involves a total pullout when NATO operations end in 2014.
Afghan President Hamid Karzai and President Obama are scheduled to meet on Friday in Washington.