Josh Earnest said the closure of the Cuban detention camp was a national security interest.
It was one of the first directives President Barack Obama ordered two months after he was elected in 2008.
Inmates have slowly been transferred out and at the start of the year, 122 men were left.
The peak population in 2003 was 684.
Mr Earnest said the administration was "in the final stages of drafting a plan to safely and responsibly (close) the prison at Guantanamo Bay and to present that to Congress".
He added: "That has been something that our national security officials have been working on for quite some time, primarily because it is a priority of the president."
In 2009, President Obama admitted the January 2010 deadline he had set for closing the counter-terrorism facility would be missed.
Since then, Congress bipartisan opposition has meant the transfer of prisoners to the US has been blocked.
Some have been considered too dangerous to be released, but the US holds no evidence that can be used in civilian or military trials against them.
The US has slowly been sending prisoners back to their home countries or to third countries, a process Mr Earnest said needs to continue if the facility is to shut.
The camp was established in 2002 by the Bush administration to detain the most dangerous suspects for interrogation and the prosecution of war crimes.
Controversy has centred around the period of time detainees have been held without charge and the use of interrogation techniques.
The White House is in the "final stages" of drafting a plan to close the controversial US military prison Guantanamo Bay, a spokesman has said.