Rumours of a possible female Doctor date back into the 1980s, but no actress has ever landed the role aside from Arabella Weir in a non-canonical audio play.
Smith discussed the possibility of The Doctor shifting sexes while speaking to reporters recently, according to The Mary Sue.
"I think there are many actresses that could play it because there are so many wonderful actresses," he said. "I mean, it would change the role because she would be a woman so when you put her in a room full of men, it's a different scenario than if you put a man in a room full of men, because she's a different sex."
Smith continued: "Would it change the fundamentals of the character? No. But it's an interesting idea, if the Doctor's a woman, does she have a Doctor baby? Is there a mini-Doctor? I don't know, who knows?"
The Eleventh Doctor actor went on to suggest Charlize Theron as the ideal female Time Lord, but added that it's unlikely to happen.
"Oh gosh, so many, so many could play her. It depends on what age you would want," he explained. "It could be... Charlize Theron is pretty kick-ass, isn't she? They just have to find a brilliant actress. I never see that happening any time soon to be honest."
Smith previously raised the casting of legendary actress Dame Diana Rigg in a 2013 episode, calling the legendary actress "totally wonderful".
Doctor Who airs on Saturday (September 8) on BBC One and BBC America with 'Dinosaurs on a Spaceship'.
Watch a trailer for 'Dinosaurs on a Spaceship' below: