Spike Lee is to direct the movie, as yet untitled, which is being written by John Ridley, the entertainment industry trade newspaper said Thursday.
Barry was mayor from 1979 to 1991 and 1995 to 1999. He is currently a member of the Washington City Council.
Murphy made headlines last month when he backed out of plans to serve as host of February's 84th Academy Awards show.
The comedian's decision came a day after his "Tower Heist" director Brett Ratner resigned as the ceremony's producer, following criticism he received for making a homophobic remark during a public question and answer session for the big-screen comedy.
Ratner later apologized for saying "rehearsal is for fags," but his critics still called for him to be ousted as Oscar producer.
Celebrity Families of 2014 [PHOTOS]