Morgan, who also penned the screenplays for Frost/Nixon and Bush-Blair drama The Special Relationship, is in negotiations to write the film from producer Jerry Weintraub.
Hefner tweeted yesterday: "I had a good meeting today with screenwriter Peter Morgan discussing a film about my life."
Morgan's last writing credit was on Fernando Meirelles's 360, which opened last year's London Film Festival and is set for release in the UK on August 10.
He also penned Ron Howard's upcoming Formula 1 drama Rush.
Watch Morgan speaking to Digital Spy about 360 below: