Obama will first present a long-awaited plan to Congress about how to close the facility, and seek its approval, McDonough said in an interview. If Congress fails to act, the White House will determine what steps to take, he said.
"He feels an obligation to the next president. He will fix this so that they don't have to be confronted with the same set of challenges," McDonough said.
Obama pledged during the 2008 presidential election campaign that he would close the military prison, which housed foreign terrorism suspects after the Sept. 11, 2001, attacks on the United States.
That pledge, still unfilled, has been a feature of his annual State of the Union addresses to the nation ever since.
Obama has said the facility has been used as a recruiting tool in propaganda from groups like al Qaeda, and also is far too costly to maintain. There are 104 detainees left at the prison.
Where possible, his administration has transferred detainees to other countries. But there is a small number of detainees who the administration says it would like to detain in a U.S. facility for national security reasons.
Congress has explicitly banned the transfer of detainees to the United States.
McDonough declined to say whether Obama would close the prison using his own executive powers if Congress rejects his plan.
"I'm not an if-then guy," he said.
(Reporting by Roberta Rampton and Andy Sullivan; Editing by Raissa Kasolowsky)
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