The 63-year-old, who is in Australia for the Doctor Who Symphonic Spectacular, says the character is an important role model for young boys.
He also said the Doctor-companion dynamic might not work with a female running the show.
"He's (the Doctor) not always certain about what he's doing and he's usually accompanied by a very strong female companion.
"If you reverse that, it seems to me you have an uncertain... female doctor with a very strong male companion... and that does seem to be very unbalanced."
There was speculation about the possibility of a female lead before the appointment of Peter Capaldi as the 12th doctor in 2013.
Though Davison doubts a woman in control of the Tardis would be appropriate, he says he's sure the character will one day be non-Caucasian.
But, the actor to break the mould will have to do so completely on merit, he said.
"Whether or not you have a black or ethnic actor playing Doctor Who is entirely down to the best actor for the role," he said.
"I don't think it should just be about 'let's pick a black actor just for the sake of doing it'."
"Probably, there were names (of non-caucasian actors) on the shortlist last time (the new doctor was picked) so I'm sure it will happen."
Davison's daughter, Georgia Moffett, who is married to tenth doctor David Tennant, once played a female time lord on the show.
The actor, who was cast in Law and Order UK after his Doctor Who stint, says he'd like female time lords other than the doctor to play a bigger part.
The Doctor Who Symphonic Spectacular featuring Davison, Daleks and Cybermen will next play in Perth on January 31.
- AAP
