The Girl with the Dragon Tattoo director is rumoured to have been targeted for the long-awaited historical remake.
Fincher did not confirm his involvement, but was willing to detail his thoughts about the project.
"That's something I would love to do with Angie [Jolie]," he told MTV News. "It's something that was brought to me that you have to take seriously.
"[Producer Scott Rudin] has this wonderful book, and hopefully [screenwriter Eric Roth] can find a way in. I'm not interested in a giant sword-and-sandal epic. We've seen scope; everyone knows we can fake that.
"That stuff doesn't impress in the way that it did even ten years ago. We expect that from Starz [now]. So that's not the reason to do that. What is it about this character that has purchased this place in our history and imagination that is relatable today?"
Jolie has said that her take on Cleopatra will not portray the Egyptian monarch as a "sex symbol".