Behind thickets of beech trees, overgrown with nettles and beside a blue lake an hour north of Berlin, a villa that once belonged to a Nazi mastermind quietly rots.

No one knows what to do with the estate beside the Bogensee lake in Brandenburg. It was built for Joseph Goebbels, the Nazi propaganda minister, by his grateful country just before the start of World War II. Owned by the State of Berlin today, it has sat moldering expensively on the public’s tab, along with a set of dramatic dormitories built later by the Communist Party to house an indoctrination school. It is a nearly 20-acre campus that echoes with the pasts of two totalitarian regimes.

Too burdensome for the state to continue carrying, prohibitively expensive for most real estate prospectors and tainted by history, Berlin has given up on selling or developing it.

Instead, it has offered to give the Nazi mansion away, free. (The taker, of course, would be subject to the government’s approval.)

In exasperated comments made to Parliament this spring, Stefan Evers, the state’s senator for finance, made the pitch — take it off our hands, or we will tear it down — setting off a flurry of interest in prospective takers from around the globe.