The pair will be working with Warner Bros on the new project and Kieran and Michele Mulroney have been signed up as writers, according to The Hollywood Reporter.
The story will follow the classic 1831 tale by Victor Hugo of the hunchbacked bell-ringer Quasimodo who falls for the gypsy Esmeralda.
The story was first made into a film called Esmeralda in 1905 while the most well-known version is probably Disney's animated version, which was released in 1997.
A live-action film was also released the same year starring actress Salma Hayek.
Brolin is set to star in the movie as well as produce while Burton is yet to sign a deal as he is reportedly waiting for the outcome of the script.