The 39-year-old actor has already played baseball great Jackie Robinson in "42" and soul legend James Brown in "Get On Up", and now he is preparing to tell Marshall's story in director Reginald Hudlin's new project, reported Deadline.
The film will focus on a career-defining case in Marshall's early days as a young lawyer, before "World War Two", when he was sent to Connecticut to defend a black chauffeur against his wealthy employer's allegations of sexual assault and attempted murder.
Marshall went on to become the first African-American judge appointed to the Supreme Court in 1967. He died in 1993.
The film will begin production in Los Angeles later this week before taking a break for the holidays and awards season, during which Hudlin will serve as a producer for the Oscars in February.
Marshall and Friedman's estate executors have given their backing to the project.