The ladies are reportedly on a shortlist being considered by Sir Andrew Lloyd Webber, who composed the music for his version of the 1950 film classic.
London's Daily Telegraph reports all three stars have been in discussions about taking on the role of Desmond, played famously by Gloria Swanson.
Close played the role onstage in Los Angeles and originated the role on Broadway, while Streisand has recorded versions of Sunset Boulevard ballads As If We Never Said Goodbye and With One Look.
Ewan McGregor and Hugh Jackman are reportedly favoured for the role of screenwriter Joe Gillis in the musical remake.
Source: WENN