But he is yet to receive the recommendation from his top US commander in Afghanistan General David Petraeus, a presidential spokesman said.
"That(drawdown of troops) will obviously be a decision he makes relatively soon in keeping with the commitment he made when he announced his Af-Pak strategy back in December of 2009, that a drawdown would begin in July of 2011," White House Press Secretary Jay Carney told reporters.
Obama is yet to make a decision on the numbers. "We have always said that it would be real. There were skeptics who suggested at the time when President announced his policy that the July 2011 date for the beginning of a drawdown was not real. It will, in fact, begin then," he said.
"The President is going to make his decision, as he has said all along, based on conditions on the ground, not whether or not there will be a drawdown, or the beginning of a drawdown, but the size and scope and pace of the drawdown," Carney said.
Noting that Obama would make the decision fairly soon, Carney said in an interview today Obama talked about the fact that this will be a summer of transition and has talked about some of the progress we have made in the mission, including obviously the elimination of Osama bin Laden.
"The fact that we have taken the fight to al Qaeda effectively, and have al Qaeda back on its heels; there has been some stabilisation in Afghanistan, some real progress, that our mission there has achieved.
"It`s part of a process that is underway of transferring security lead to the Afghan national security forces. That process obviously will reach its culmination, as promised in Portugal, at Lisbon, at the NATO conference, will reach its culmination in 2014," Carney said.
Earlier, Obama held his monthly Af-Pak situation room meeting with his top national security team.
During which, the President received briefings on progress in implementing US strategy for Pakistan and Afghanistan following the death of Osama bin Laden.
By video, Defense Secretary Robert Gates briefed the President on his recent trip to Afghanistan.
"The group also discussed our strategic partnership with Afghanistan and the progress being made to build and sustain the Afghan National Security Forces, and the President`s upcoming videoconference with President Karzai on Wednesday, June 8," a White House statement said.
"The President also received an update on our efforts to ensure effective cooperation with Pakistan against al Qaeda and other violent extremists," it said.