Earnest said the best route for closing the prison would be winning Congressional approval to do so.
The White House said last month that it would soon be sending a plan to Congress to close the prison, which President Barack Obama has made a priority.
Asked if Obama would consider taking executive action to close the prison if Congress blocks him, Earnest said, "The president and his team are always considering a wide array of options.
"But the fact is the best way for us to do this is for members of Congress of both parties to work effectively with the administration," Earnest said.
Closing the prison is likely to involve transferring some detainees to prisons within the United States. Republicans have barred those transfers and already have begun to push back against suggestions floated by the administration as possible host sites.
Defense Secretary Ash Carter said on Aug. 20 that a U.S. army delegation had visited a potential facility in Leavenworth, Kansas, and would soon tour the U.S. Naval Consolidated Brig at Charleston, South Carolina.
In response, Republican South Carolina Governor Nikki Haley said at a news conference, "We are not going to allow any terrorists" to be housed in Charleston
