According to The Hollywood Reporter, the Great Gatsby star has emerged as the top choice to play the US politician in the film, which focuses on her formative years working on the Richard Nixon impeachment hearings in the 70s, before she married fellow politician Bill Clinton.
Jessica Chastain has already denied she is taking the role, while Scarlett Johansson, Reese Witherspoon, Amanda Seyfried and Emma Stone are also rumoured to be in the running.
James Ponsoldt is set to take the reins for the movie, which has been written by Young Il-Kim, and will reportedly be getting in touch with Carey to discuss the project.
Carey - who was nominated for an Oscar for her performance in An Education - stars in Baz Luhrmann's glamorous take on F Scott Fitzgerald's The Great Gatsby alongside Leonardo DiCaprio and Tobey Maguire.
The 28-year-old, who is married to Mumford And Sons frontman Marcus Mumford, will next star in Ethan and Joel Coen's Inside Llewyn Davis.