According to Deadline, MGM has offered Kinnaman the title role in the sci-fi.
Russell Crowe and Michael Fassbender are among the actors who have previously been rumoured to play the character originated by Peter Weller.
The film is being directed by Jose Padilha, and was penned by writer Josh Zetumer.
Padilha has said that the new film will "fill in gaps" present in the original 1987 film, presenting a more realistic universe.
Kinnaman, who starred on the AMC series The Killing, was most recently featured as a villain in the Denzel Washington thriller Safe House.
Watch the trailer for Safe House below: