Barnes is the focus of director Marc Levin's new documentary "Mr. Untouchable" and a supporting character played by Cuba Gooding Jr. in the feature film "American Gangster."
Whitaker, who won an Oscar for his work in "The Last King of Scotland," has directed the films "Hope Floats" and "Waiting to Exhale."
He will soon be seen opposite "American Gangster" star Denzel Washington in Washington's directorial effort "The Great Debaters."
The Showtime series has no official connection to "Gangster" and Gooding isn't involved in the TV drama, the trade paper said.
Whitaker has collaborated with Showtime before, most recently starring in the 2003 TV movie "Deacons for Defense."
He also executive produced and starred in the Anne Rice 2001 mini-series "Feast of All Saints" and in starred in the 1994 movie "Lush Life."
Whitaker and Levin will executive produce the Showtime series, with "Law & Order: Special Victims Unit" veteran David Burke serving as writer and executive producer, Variety.com said.