The Pirates of the Caribbean star confirmed last year that she had auditioned and begun singing lessons, reports the Telegraph. However, she has since been told that she has an American rival for the part.
Sir Cameron said: "I have two actresses as potential Elizas, one British, the other American. You'd know their names, but I'm not letting on."
Emma Thompson is writing the script for the film, which Stephen Daldry is expected to direct. Daniel Craig may be Professor Henry Higgins.