One official said the troops could be out by summer, but no final decision has been made.
The officials spoke on condition of anonymity to discuss internal deliberations.
U.S. troops stormed into Afghanistan in November 2001 in an invasion triggered by the Sept. 11 attacks.
Since then, America has lost more than 2,400 soldiers and spent more than $900 billion in its longest war. Three U.S. presidents have pledged to bring peace to Afghanistan, either by adding or withdrawing troops, by engaging the Taliban or shunning them, and by struggling to combat widespread corruption in the government.
The U.S. and NATO formally concluded their combat mission in 2014, but American and allied troops remain, conducting strikes on the Islamic State group and the Taliban and working to train and build the Afghan military.
Taliban insurgents, however, control nearly half of Afghanistan and are more powerful than at any time since a 2001 U.S.-led invasion. They carry out near-daily attacks, mainly targeting security forces and government officials.
In recent months, however, there has been a renewed effort to make progress on peace talks with the Taliban. Officials now worry that any move to withdraw U.S. troops this year could dampen those prospects and simply encourage the Taliban to wait it out until they can take advantage of the gaps when the forces leave.