An announcement in this regard is expected to be made by Obama tomorrow.
However, any US troop presence in Afghanistan after 2014 is subject to signing of the Bilateral Security Agreement (BSA) by the new Afghan president, a senior administration official said.
Afghan President Hamid Karzai has refused to authorise the BSA, that should be signed by Karzai's successor to become effective.
Ashraf Ghani and Abdullah Abdullah are the two candidates in a June runoff election to become the next Afghan president.
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"By the end of 2015, we would reduce that presence by roughly half, consolidating US troops in Kabul and on Bagram Airfield. And one year later, by the end of 2016, we will draw down to a normal Embassy presence with a security assistance office in Kabul, as we have done in Iraq," the official said.
Both Afghan presidential candidates recently reiterated their intentions to sign the agreement quickly if elected, the official pointed out.
"He (Obama) will announce that our combat mission will be over by the end of 2014. He will make clear that we are open to continued efforts in Afghanistan on two narrow missions after 2014: training Afghan Forces and supporting CT (counterterrorism) operations against the remnants of al Qaeda.
"We will only sustain a military presence after 2014 if the Afghan government signs the Bilateral Security Agreement," the official said.
The US and NATO plan to withdraw most of their forces ahead of a year-end deadline. Obama wants to keep a small number of US troops in Afghanistan after 2014 to train Afghan security forces and support counterterrorism missions.