President Barack Obama made the closure of the controversial offshore prison a priority when he took office in 2009, but the plan has faced numerous setbacks, including Congress blocking the transfer of detainees to US prisons.
"The administration is in fact in the final stages of drafting a plan to safely and responsibly (close) the prison at Guantanamo Bay and to present that to Congress," Earnest said.
"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."
The US has slowly been sending prisoners back to their home countries or to third countries, something that needs to continue if the facility is to shut, Earnest said.
Just under half of the detainees remaining have been cleared to leave but have yet to be resettled or repatriated.