The Doctor has been played by a male actor since 1963 but Davies admitted that a female could take over the iconic part if people supported the idea.
"I think the more it's talked about, the more likely it is to happen," he said at a press conference to promote the upcoming Christmas special The Next Doctor.
When asked which actresses he would like to see in the role, he answered: "Lesley Sharp or Catherine Zeta Jones."
Current Doctor David Tennant is bowing out from the show next year after five years in the role, but Davies warned that replacing him could be a lengthy progress.
"It's a big deal to set up," he said. "Whoever becomes the Doctor has got to take on a whole life. It's a lot of soul-searching to do."
Last month David Morrissey revealed that he would "jump" at the chance to portray the Time Lord, fuelling speculation that he had been shortlisted for the part.