The actress - who had been linked to the role - also ruled herself out of consideration during an interview with 'Daybreak', as she supported the idea of the part being awarded to a woman.
She said: "I’m not going to be the first female Doctor Who, no, no, no, absolutely not, I absolutely wouldn’t contemplate that.
"But I do think it’s well over-time to have a female Doctor Who. I think a gay, black female Doctor Who would be the best of all."
Matt announced he was quitting as The Doctor last month, and is set to bow out in the Christmas special.