The Golden Globe-winning actress is in talks to appear in the modern-day adaptation of the play, to be adapted by Shame and The Iron Lady screenwriter Abi Morgan, reported The Wrap.
No director appears to be attached to the new version, which will be set in mid-20th century Italy.
Les Miserables producer Debra Hayward will produce the film with Working Title.
Anne - who is also up for a best supporting actress Oscar for her performance as Fantine in Tom Hooper's Les Miserables - had been set to star opposite Chris Hemsworth in Steven Spielberg's sci-fi adaptation Robopocalypse, which has been pushed back.
The 30-year-old has long been attached to a big-screen adaptation of Gerard Clarke's Judy Garland biography, although that has yet to move into the pre-production stage.