The Iron Man star has been linked to the lead role in a BBC drama based on the life of the German actress, who died in 1992.
Dietrich's personal life was just as colourful as her high profile film roles - she was bisexual and allegedly battled a dependency on drink and drugs throughout her career. She was also rumoured have enjoyed a string of love affairs with stars including Frank Sinatra, Yul Brynner and John Wayne.
Scriptwriter Andrew Davies has based the film on a 1992 biography of Dietrich by the actress' daughter Maria Riva.