Recent reports claimed that the Gavin & Stacey actress was lined up to star in the BBC One show but Page has now denied the claims.
"It's not true," she told PA. "A friend was telling me about that. I was like, 'I wish it was true'.
"I think I've got to be the only Welsh actress who has never been in Doctor Who so if someone would like me to be in Doctor Who I would love the part."
Page's Gavin & Stacey star James Corden will appear in a future episode of the series.