Chastain: ‘No, that’s actually not true. I found out about the project online, but, yeah, there’s a lot of stuff out there.’
It's not a flat out denial, but considering her busy schedule it's not surprising she doesn't especially interested. She has Christopher Nolan's Interstellar coming up, along with Guillermo Del Toro's Crimson Peak. She just recently wrapped up Liv Ullman's Miss Julie, and also has The Zookeeper's Wife to film at some point.
So that leaves Amanda Seyfried, Scarlett Johansson, and Reese Witherspoon as the other candidates for the Clinton role.