Production on the film began on Monday and Beatty, who has written the script, is directing and starring as Hughes, according to Deadline.com.
The untitled film will centre on a love affair between Hughes' assistant, who will be played by Blue Jasmine actor Alden Ehrenreich, and a socialite portrayed by Lily Collins.
Beatty's wife Annette Bening, Matthew Broderick and Jack Nicholson are all rumoured to be starring in the film as well.
Rush Hour director Brett Ratner is producing the movie along with Beatty.
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