Bale would play Cheney, who served as vice president under George W. Bush, with Carell as two-time Secretary of Defense Donald Rumsfeld and Adams as Cheney's wife, Lynne Cheney. Bale and Carell previously worked with McKay on The Big Short.
McKay will write, direct and produce the movie, with Brad Pitt as a co-producer. The project has yet to receive a green light from Paramount Pictures, although Deadline reported McKay plans to start filming in September.
"I've always found Cheney fascinating," the director told Deadline in November. "Questions of what drove him, what his beliefs were."
Cheney served as White House Chief of Staff under president Gerald Ford, and was later chosen as Secretary of Defense during George H. W. Bush's presidency. He became the chairman and CEO of Halliburton oil in 1995 before being sworn in as vice president in 2001.
"Once we started digging, I was astounded at how much he had shaped modern America's place in the world and how shocking the methods were by which he gained his power," McKay said.
Bale will next appear in The Promise with Oscar Isaac. He is also slated for Hostiles with Ben Foster and Rosamund Pike, and will voice Bagheera in a Warner Bros. adaptation of The Jungle Book.