Charlie Stratton, who helmed a 1995 version of the play, will direct the film from his adapted script.
The story, set in Paris, revolves around a young woman who embarks on affair and conspires with the man to murder her husband - who is also her first cousin. Close will play the husband's mother.
She won Tony Awards for her roles in The Real Thing, Death and the Maiden, and Sunset Boulevard, and also received a Tony nomination for Barnum.
She is a 2012 Oscar nominee for Albert Nobbs, and received prior nominations for Dangerous Liaisons, Fatal Attraction, The Natural, The Big Chill, and The World According to Garp. She also stars on the TV series Damages.