That's about half the U.S. forces currently serving there, and marks the next phase in the administration's plans to formally finish the war by the end of 2014.
The U.S. is still finalizing plans for the size and scope of its military presence after the war ends. The White House has said it would be open to leaving no troops in Afghanistan, though it's likely that a small presence will remain, in keeping with the Pentagon's preferences.
The people familiar with Obama's remarks requested anonymity in order to discuss the troop drawdown ahead of the president.
Obama discussed the next phases of the drawdown with Afghan President Hamid Karzai during a day-long meeting in Washington last month, the first meeting between the two leaders since Obama's re-election. The two leaders agreed to accelerate their timetable for putting Afghan forces in the lead combat role nationwide, moving that transition up from the summer to the spring.
Obama will announce the troop drawdown and the future of the U.S. role in Afghanistan during a joint session of Congress that is otherwise expected to be dominated by the economy and other domestic issues.
Foreign policy has intruded in recent days, however, and the White House quickly condemned North Korea early Tuesday for its nuclear launch hours before Obama's address. The president is expected to make further remarks on this in his primetime speech.
Some private security analysts, as well as some Pentagon officials, worry that pulling out of Afghanistan too quickly will leave the battle-scarred country vulnerable to collapse. In a worst-case scenario, that could allow the Taliban to regain power and revert to the role they played in the years before 9/11 as protectors of al-Qaida terrorists bent on striking the U.S.
Many Americans, however, are weary of the war, according to public opinion polls, and are skeptical of any claim that Afghanistan is worth more U.S. blood.