Proposals are being drawn up by the Liberal-controlled council in Newbury, Berkshire, together with local historians, military-vehicle enthusiasts and the half-dozen women still remaining in a camp at the main gates of the base.
The museum, which would be in missile bunkers and control rooms that once belonged to the US Air Force's 501st Tactical Missile Wing, would record the history of the base and its part in the Cold War. It would be Britain's second museum to commemorate anti-war activism; a derelict Bradford warehouse is to become the National Peace Museum.
Newbury District Council hopes to attract European Commission funds, as well as Millennium Fund grants.
At the height of the Greenham Common campaign in 1981, the perimeter was encircled by 35,000 protesters holding hands. Those remaining have been reluctant to leave until the site's future is resolved. The council, which has formed a trust with local businesses to buy the airfield from the Ministry of Defence, plans to convert most of its 800 acres back to heathland, but the hangars, control rooms and offices would be let out for sport, leisure and industrial use. Music, printing and light engineering companies are already there.
Evelyn Parker, who was involved with the peace camps from the beginning, expressed support but said: "We are cautious about it. I don't think that the women would want it to be portrayed as a `peace women versus the warmongers' thing. We can talk about Cruise missiles and show pictures of spray-painted silos, but for me the Greenham Common women were about more than that. They found a quite different way of living in a community together. It was a living, social thing. I don't think you'll see that in a museum."
Greenham Common was decommissioned four years ago, but ghosts of the Cold War still lingered, Peter Gilmore of Newbury council said. "A few months ago I would have said we'd have the purchase wrapped up by the end of the year. But the Government keeps putting obstacles in front of us," he added.
One difficulty is that the Government would like to keep a set of keys, because the empty missile silos are still subject to a treaty signed by Presidents Reagan and Gorbachev, which guaranteed they could be inspected by the Soviet Union at 18 hours' notice. "Since there is nothing there for the Soviets to inspect and there are no Soviets left to do the inspection, I don't see the problem," Mr Gilmore said.
Dr Peter Van Den Dungen, a lecturer in the Department of Peace Studies at the University of Bradford, who has helped to plan the Bradford museum, said: "Striving for peace is as old as humanity, as old as war. Yet the ignorance about even the recent past is staggering. Even those in the peace movement would be hard-pressed to name two or three British Nobel laureates."
He would like to see a much bigger museum, and said of the Millennium funding: "When I see these plans that have been submitted, for great follies or Ferris wheels, none of them are as materially relevant to the Millennium as this."