The exact details of the role are being kept secret, according to Heat Vision.
Colin Farrell is to take on Arnold Schwarzenegger's role from the original as a factory worker who discovers he is a spy for either his own nation or an enemy one.
The first film saw Schwarzenegger buy the memory of travelling to Mars, but getting trapped while he is on the red planet.
Farrell recently said that the update will be much "darker" than Paul Verhoeven's 1990 movie.
Underworld helmer Len Wiseman is to direct, with negotiations still ongoing for the female lead.
Kate Beckinsale and Jessica Biel are currently in talks to play the factory worker's wife Lori and helper Melina respectively.
Hawke will next be seen in the pilot episode of the forthcoming US television show Exit Strategy, which is partially set in "real-time".