The paper attributed the report to sources close to the production.
The role of the overweight Baltimore housewife-laundress was originated by the late Divine in John Waters' 1988 film -- which was turned into a Broadway musical in 2003, with Harvey Fierstein as Edna.
Since then, Michael McKean and Bruce Vilanch have played Edna on Broadway.
"Hairspray" won nine Tony Awards, including Best Musical and Best Performance by a Lead Actor in a Musical for Fierstein.
This is not the first time there has been speculation about Travolta starring in a movie version of a Broadway hit. Some years ago, there were reports that he had the inside track to star in the title role of the film version of "The Phantom of the Opera" -- a role that eventually went to Gerrd Butler.
2014: The Year in Music [PHOTOS]