The 39-year-old 'The Master' star is in negotiations with Warner Bros for the role, reported Variety.
The casting rumour has come at a time when Phoenix's latest movie 'Her' is creating Oscar buzz.
Phoenix has delivered many critically-acclaimed performances in films like 'Gladiator', 'Walk the Line' and 'The Master', but he reportedly turned down offers to take part in blockbuster superhero movies in the past.
The 'Man of Steel' sequel is directed by Zack Snyder who helmed the first film. Henry Cavill is back as Superman, Amy Adams returns as Lois Lane, Ben Affleck is added as Batman, and Gal Gadot is brought in to portray Wonder Woman.
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