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Rex Features
The 47-year-old, who picked up this year's best supporting actress Oscar for her role in Michael Clayton, will play a foreign society matron who falls for a young chef in Milan.
The Italian-language film will be directed by Luca Guadagnino, who previously worked with Swinton in 1999's The Protagonists.
He said the film is about "the irreparable consequences brought about by love in a high-bourgeois family".
Shooting is scheduled to begin in Milan this summer.
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