The actress, who made her New York stage bow in A View From The Bridge in 2010 - and picked up a Tony Award for her performance, is slated to take on the role made famous by the late Elizabeth Taylor in the 1958 movie adaptation of the play.
She tells Variety, ""I'm close to making a deal on it. I cannot wait absolutely to get to it. I'm exhilarated, I'm terrified, but I think in a good way.""
The actress' The Avengers co-star, Jeremy Renner, has also been linked to a role in the production.