President Barack Obama made shuttering the Cuba-based prison a priority when he took office in 2009, but Congress has opposed measures to transfer detainees to the US mainland.
The White House is currently putting finishing touches on a new plan to close Guantanamo, which will be presented to lawmakers for review.
The military prisons in focus are at Fort Leavenworth in Kansas and the Navy Brig in Charleston, South Carolina.
The team will be in Charleston next week, Davis said, adding it is also expected to visit some non-Department of Defense sites.
Guantanamo opened in January 2002 on the heels of the September 11, 2001 attacks on New York's World Trade Center and on the Pentagon in Washington.
After reaching a peak of 680 war on terror detainees in 2003, there are 116 detainees remaining.