The director, 62, is said to be in talks with Showtime, an American cable television company, and DreamWorks TV about the series, which has yet to be given a title.
Spielberg also intends to take the production itself on to the stage.
Variety claimed that Spielberg had been developing the concept for the show "for years", and was hoping to recruit producers Craig Zadan and Neil Meron, who were behind taking Chicago and Hairspray from the stage to the big screen.
He is also said to be interested in getting on board Marc Shaiman and Scott Wittman, who co-wrote the score for Hairspray and the musical adaptation of Spielberg's 2002 film Catch Me If You Can, which starred Leonardo DiCaprio.
The series will look at all aspects of creating a musical and taking it to the stage, from writing the songs to convincing investors, as well as the delving into the personal lives of the main players like the actors and producers.
It is understood Spielberg wants to create a scripted series, as opposed to a reality television programme or documentary, although the fact that it will be made in tandem with the musical could create problems.
If successful, it could be rolled out to last more than one series, looking at new productions in future years.
Spokesmen for Showtime and DreamWorks TV declined to comment.
Source - http://www.telegraph.co.uk/culture/film/film-news/6229702/Steven-Spielberg-planning-TV-show-about-a-musical.html