Pitt previously headlined the 2004 blockbuster "Troy," which was based on another Homer work, "The Illiad," and directed by Wolfgang Petersen.
The entertainment industry trade newspaper said the studio wants to make a futuristic version of "The Odyssey" set in outer space.
The recent movies "O Brother, Where Art Thou" and "Cold Mountain," which both followed heroes on a long journey home, were also inspired by "The Odyssey."
Pitt will soon be seen in the films "The Curious Case of Benjamin Button" and "Tree of Life." He recently began work on Quentin Tarantino's "Inglourious Basterds."