The Argo helmer is close to agreeing a deal with Pearl Street and Appian Way to bring the book to the big screen, according to The Hollywood Reporter.
Live By Night is a Prohibition-era tale of a Boston man who betrays his police officer father and becomes a career criminal, rising up the ranks in the world of organised crime.
Meanwhile, Argo opened in US cinemas today (October 12) and is due to arrive in the UK on November 7. The project is Affleck's directorial follow-up to the award-winning 2010 crime drama The Town.
Affleck's Argo co-star Bryan Cranston recently praised his directorial skills, describing him as "bright" and "personable".
It is yet to be confirmed whether Live By Night will be Affleck's next project.
Watch a trailer for Argo below: