The Harry Potter star may join the director for his follow-up to Moonrise Kingdom, reports Variety.
Fiennes would play the hotel's composed concierge M Gustave.
Regular Anderson collaborator Bill Murray will feature in the movie alongside Angela Lansbury and Jude Law, who have not previously worked with the director.
Details of the film, which Anderson will produce with Indian Paintbrush's Scott Rudin and Steven Rales, remain under wraps.
Fiennes will next be seen in Skyfall, Great Expectations and 2013's The Invisible Woman, which he will also direct.