The Tower Heist star would play former Washington DC mayor Marion Barry in the project, according to The Hollywood Reporter.
Barry served as the US capital's mayor from 1979 to 1991, and again from 1995 to 1999. In 1990, the Democratic politician was arrested on drug charges and served six months in prison.
Spike Lee is attached to direct the biopic, while Red Tails scribe John Ridley will pen the script. The pair would also executive produce alongside Murphy.
Murphy was due to host the 2012 Academy Awards, but later dropped out and was replaced by Billy Crystal.
He will next appear opposite Kerry Washington and Alison Janney in film comedy A Thousand Words.
> Oscars 2012: How Eddie Murphy, Brett Ratner lost the Academy Awards
Watch the trailer for Eddie Murphy's A Thousand Words below: