Davis's nephew, Vince Wilburn, told reporters about the plans last night after Davis was inducted into the Rock and Roll Hall of Fame in Cleveland.
The movie, Wilburn said, "could touch on many things: the way he changed music in different decades, from Bird [Charlie Parker] to bebop to hip-hop and in between."
An actor has not been chosen to play Davis, Wilburn said, "but Don Cheadle's name keeps coming up." Cheadle has been critically acclaimed for his performances in Hotel Rwanda, Crash, and other films, and bears a slight resemblance to Davis. He was not available for comment.
The family has spoken to Antoine Fuqua, the director of Training Day, about directing the film.
The film would apparently be produced by Sony Pictures, the corporate cousin of Columbia Records, Davis's longtime label, but the studio declined to discuss it, E! said.
Davis played bebop with Charlie Parker in the 1940s before leading important cool jazz, modal jazz, and hard bop groups in the '50s and '60s. He was honored by the Rock and Roll Hall of Fame for his contributions to jazz-rock fusion on such albums as Bitches Brew (1970).