The Gladiator and Superman: Man of Steel star is expected to be confirmed for Black Swan director Aronofsky's biblical epic in an official announcement later this week, according to Deadline.
Prometheus actor Michael Fassbender and Batman: The Dark Knight Rises star Christian Bale were both previously linked with the movie's lead role.
Paramount Pictures and New Regency Productions are behind the project, with screenwriters Ari Handel (The Fountain) and John Logan (Gladiator) on board.
Aronofsky has also been working on a Noah comic book with illustrations from Nico Henrichon.
The director has previously spoken of his fascination with the tale of Noah, describing him as a "dark, complicated character", and has promised to make "a big event film".
Filming on Noah is now due to begin in July, and the movie has a rumoured $130 million (£82 million) budget.
> 'Black Swan's Darren Aronofsky directs four anti-meth videos: Watch