Stone, who has worked on movies such as Wall Street, JFK and W, is expected to executive produce and direct the project.
Deadline says that the show focuses on 'Darkhorses', a secret group of people who make up fake news stories to help their clients.
The project is being written by Adam Gibgot, who has previously collaborated with the illusionist David Blaine.
FX is also currently thought to be developing a drama series with Friday Night Lights star Connie Britton.
> FX cancels Lights Out