The writer's former New Yorker colleague Tina Brown will be executive producer on the project, according to The Hollywood Reporter.
The film will centre around the late Pulitzer Prize winner's relationship with prisoner Jack Abbot.
Mailer mentored the convicted killer and helped him gain parole and publish his own book In the Belly of the Beast.
Mailer's reputation was subsequently put in jeopardy when Abbot killed a man after his release.
The script is being penned by Wall Street: Money Never Sleeps writer Stephen Schiff.
Brown, a founder of the Norman Mailer Center, brought the project to HBO with Norman's son Michael Mailer.