The restaurant in Greek Street was opened by restaurateur Victor Sassie in 1953 and became a restaurant of choice for the political left with Labour MPs Michael Foot, Ian Mikardo, Barbara Castle and Roy Hattersley all becoming regulars along with columnists from Fleet Street.
Property agent Christie & Co is selling the site's leasehold off a guide price of £500k.
Director and head of restaurants Simon Chaplin said: "The Gay Hussar has a special place in the heart and political history of London. Whilst its infamous days as the venue where various political machinations took place may be behind it, it is still today one of London’s most unusual and popular restaurants. With this, and its unique history, we anticipate a great deal of interest.”