Allan Glaser, Hunters longtime partner, and publicist Neil Koenigsberg are also producing the Paramount project.
The book previously inspired a 2015 documentary, which Glaser also produced.
Pulitzer Prize-winning playwright Doug Wright is attached to write the screenplay.
Credit: Silver Screen Collection/Getty Images; Archive Photos/Getty Images
The project does not yet have a director or stars on board.
Hunter will turn 87 in July.
Perkins died from AIDS-related pneumonia in 1992.
The Hollywood Reporterfirst reportedthe news.
