While no final decision on numbers has been made, the officials said the administration is poised to slow withdrawal plans and probably will allow many of the 9,800 American troops to remain well into next year.
There also are discussions about keeping a steady number of counterterrorism troops into 2015, including options under which some would remain in the country or be nearby beyond 2016.
Officials say President Barack Obama probably will use a Washington visit by Afghan President Ashraf Ghani this month as the time to announce his decision on a new withdrawal timeline.
US officials familiar with the debate said it's not clear yet whether the White House will agree to a small, symbolic decrease by the end of this year or insist on a larger cut.
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In recent weeks, Pentagon leaders, including Defense Secretary Ash Carter, have acknowledged the discussions about slowing the pace of troop withdrawal.
But they increasingly are confident that the military will get its way and keep a robust force in Afghanistan beyond year's end.
The administration, however, has shown no inclination so far for going beyond 2016; that's a hard line drawn by the president when he announced the withdrawal plan.
The 2016 deadline is considered a politically crucial national security goal for Obama, who promised to get all troops out by the end of his presidency, ending America's longest war.
Military leaders want to keep what they consider a "modest" number of troops in Afghanistan longer in order to protect America's investment and provide as much training and advice as possible to Afghan forces.
Maintaining a more stable number of troops, military leaders have argued, would allow better support of the Afghans during this summer's fighting season and better prepare them for 2016 battles.