The "Gladiator" star is tipped to take on the role of the media mogul in a movie based on "Good Times, Bad Times", the memoirs of former Sunday Times editor Harold Evans, reported Contactmusic.
"You have to be brave to play someone like Murdoch. Russell can do it," a source said.
Actor Colin Firth is believed to be up for the role as Harold, but no deals are yet in place.
"The film will be a drama, either for the big screen or television. It is very early days as the option deal with Harry was only just completed. No actors or even writers have been signed up yet," said Leon Lecash, creative director of the film.