Cinemavault is handling sales.
The project is Buscemi's fourth as a director and it played in Sundance and Berlin.
The drama follows a fading political journalist who has to interview a popular soap actress. Bruce Weiss and Gijs van de Westelaken produced.
The Works Distribution managing director Mick Southworth said: 'We are delighted to be working with Cinemavault again on such a high calibre title. Sienna Miller is loved in the UK and is superbly directed here by Steve Buscemi.'