UPDATED: Thu, 9th August 2012
Countering this story is a report from Deadline's Mike Fleming. He states:
I’m calling bullshit on this big Variety scoop today that implies Warner Bros will get Ben Affleck as director of its Justice League film. This is a story I checked out days ago, and didn’t run when Affleck’s reps stated that it was not going to happen with him.
Just because the studio wants Affleck doesn’t mean he will do the movie, and several sources tell me he might take a meeting, but that’s it.
We'll be keeping an eye on developments on this.
http://m.deadline.com/2012/08/ben-affleck-on-justice-league-his-camp-says-no/

Variety is reporting that Warner Bros are approaching Ben Affleck to direct the planned Justice League movie (with a likely release date of 2015). Affleck is high on the studio's list of filmmakers who can be trusted with such a film. So far, Affleck is the only candidate who's been sent Will Beall's "Justice League" script.
Variety suggest:
Affleck has made it clear that going forward, he's only interested in directing films in which he also stars -- "The Town" and "Argo" are proof of that -- so its likely that if this pairing ever came to fruition, he would likely don a suit of his own. DC Entertainment, Warner Bros. and Affleck's reps declined to comment.
That in itself is interesting!
How it will affect other projects Affleck is working on and planning at the moment remains to be seen - and may well decide the outcome of any involvement by Affleck in a Justice League flick. We should know soon enough though...the article suggests a meeting between Warners and Affleck could happen within days.
Read more here [LINK]