Directed by Jim Jarmusch, Only Lovers Left Alive is a love story between two vampires who have been in love for centuries.
The film is expected to begin shooting in Germany this year, says The Hollywood Reporter.
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Jarmusch directed the 2009 crime drama The Limits of Control, which starred Swinton and Hurt along with Bill Murray, Gael Garcia Bernal and Paz de la Huerta.
Swinton, who turned in a critically-acclaimed performance in We Need to Talk About Kevin, revealed she "wasn't disappointed" when she missed out on an Oscar nomination.
She explained: "I wasn't disappointed. I didn't know for hours, but someone was telling me apparently everyone else was disappointed. I had very low expectations, so perhaps my expectations were a bit lower than everybody else."
Watch the trailer of We Need to Talk About Kevin below:
