The New York Post reports that Emily Mann will direct the revival, which will be produced by Stephen Byrd (2007's Cat on a Hot Tin Roof) and will open in early 2011.
The New York daily also says that Will Smith and Jada Pinkett Smith have been approached to play the lead roles of, respectively, Stanley and Stella Kowalski.
There has been no official announcement about a Streetcar revival.
Williams' drama concerns the faded Southern belle Blanche DuBois, who is driven to madness by her brother-in-law, Stanley Kowalski.
A Streetcar Named Desire premiered on Broadway at the Ethel Barrymore Theatre in Dec. 1947, playing 855 performances before closing in Dec. 1949. Directed by Elia Kazan, the original company boasted Jessica Tandy as Blanche, Marlon Brando as Stanley and Kim Hunter as Stella. The most recent Broadway revival — in 2005 at Studio 54 — starred John C. Reilly, Natasha Richardson and Amy Ryan.
Emily Mann is the artistic director of New Jersey's McCarter Theatre. Mann is scheduled to direct the New York City premiere of Edward Albee's Me, Myself & I starring Elizabeth Ashley and Brian Murray.