A museum chronicling the 40 years of the Cold War could be built on the site of a shuttered prison in Fairfax County.

Negotiations between the Cold War Museum and Fairfax County park officials are under way to turn a 26-acre parcel on the south end of the former D.C. Department of Corrections facility at Lorton into the museum’s first permanent home. If talks are successful, the project would be the latest step in a massive effort to overhaul the sprawling, 2,000-plus-acre Lorton reservation.