The veteran actor is in talks to take the role of Russell Crowe's nemesis in the Biblical adaptation, reports Deadline.
A number of actors - including Val Kilmer, Liev Schreiber and Liam Neeson - were said to have been considered for the role, with Aronofsky deciding he wanted someone with "grit".
Logan Lerman and Douglas Booth will play Noah's sons in the movie, with Emma Watson appearing as the latter's love interest.
Julianne Moore and Jennifer Connelly are reported to be competing for the role of Noah's wife.
Winstone was most recently seen as one of the dwarves in Snow White and the Huntsman.
Noah will begin filming in August for release on March 28, 2014.