The 42-year-old actor has been rumoured to play the Doctor since 2013, when he told The Independent: “I haven’t been and I am totally certain that I will not be asked to be the next Doctor Who.
Doctor Who fans voted Crystal Maze host Ayoade, 43, as their first pick to take over from Jodie Whittaker in a poll earlier this year.
The former My Family star left Death in Paradise a few years ago, freeing up time for him to play the Doctor.
Her theatre company Dry Write wrote on Twitter: “We can confirm that Phoebe is not the next Doctor Who.