According to Deadline, Affleck was offered the chance to helm the superhero picture by Warner Bros on the suggestion of Nolan but chose to decline the approach.
Affleck picked up an Academy Award in 1998 for co-writing Good Will Hunting with Matt Damon and his since directed the critically acclaimed dramas Gone Baby Gone and The Town. The latter, a Warner Bros-backed movie, topped the US box office last month.
Affleck portrayed former Superman star George Reeves in 2006 biopic Hollywoodland.
Darren Aronofsky, Duncan Jones, Matt Reeves and Zack Snyder have also been rumoured for the director's chair on the Nolan-steered Superman project.