Fuller also revealed that Eddie Izzard has been on set, posting a picture of the two together and writing: "Always hungry for more @eddieizzard on #HANNIBAL - here we plot our next course."
Izzard will reportedly play an asylum inmate who claims that he is an infamous serial killer.
The show will explore the early relationship between Dr Hannibal Lecter and a criminal profiler, special agent Will Graham.
Lecter will be played by Casino Royale star Mads Mikkelsen, with Hugh Dancy (The Big C) in the role of the Agent Graham. Caroline Dhavernas (Devil), Lara Jean Chorostecki (Copper) and Laurence Fishburne (The Matrix) also feature in the series.
Fuller is an executive producer on the thriller, along with Martha De Laurentiis, Katie O'Connell, Sara Colleton and Jesse Alexander.