Bale may play the former vice president of United States, while Adams is on board to play Lynne Cheney. Carell, meanwhile, is reportedly in talks to play former US congressman Donald Rumsfeld, reported Variety.
McKay will helm the movie from his own screenplay. Gary Sanchez Productions and Brad Pitt's Plan B are set to produce.
Producers and studio plan to film the biopic sometime in spring for an award-season push.
Cheney was the CEO of Halliburton Company before becoming vice president under George W. Bush between 2001 and 2009.
Bale teamed up with McKay in Oscar-nominated "The Big Short" in 2015. He will next be seen in historical drama "The Promise" and western movie "Hostiles".
Carell, meanwhile, has finished filming "Last Flag Flying" and will star in "Battle of the Sexes". Adams recently starred in critically-acclaimed "Arrival" and will reprise her role as Lois Lane in superhero movie "Justice League".
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