Anyone chosen to fill in the vacant slot left by the "Sherlock Holmes" actor is expected to play the main villain in the film, reported Los Angeles Times.
Director Gavin O'Connor is looking for an actor with an international brand "who also looks good in a hat."
Law withdrew himself from the movie because he was signed on to work with director Lynne Ramsay.
Portman will play the heroine named Jane Hammond, and Edgerton will be her sidekick Dan Frost. The story revolves around the farmer wife of an outlaw husband who, after his gang turns on him, must defend herself with the help of an old lover.