Deadline reported Monday the 30-year-old actress is in early talks to star in Chazelle's movie Babylon. Stone previously worked with Chazelle on his 2016 film La La Land and won an Academy Award for Best Actress for her role in the musical.
The Hollywood Reporter said Chazelle wrote the script and will direct Babylon, which is set in 1920s Hollywood. The film reportedly examines the movie industry's transition from silent films to talking pictures.
One of the characters in Babylon is Clara Bow, a real-life actress and Hollywood's first "It Girl." Stone is loosely attached to the role but hasn't signed an official deal.
Lionsgate, Paramount, Netflix and other studios are said to be interested in acquiring the film. Sources said Chazelle's script is 180 pages long, with the project expected to have a budget around $80 million to $100 million.
Chazelle previously worked with Lionsgate on La La Land, although sources told Variety Paramount may have a slight edge due to the new movie's large scope and budget.
Stone last starred in the Netflix miniseries Maniac. She is slated for a number of other projects, including the films Zombieland: Double Tap and Cruella.