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According to the Daily Star, the BBC wants to sign up the singer, 24, to play a villain in the series.
Scriptwriter Gareth Roberts said: "The script might end up on screen one day with Lady GaGa, who will have fallen on hard times."
A source added: "She is no stranger to dressing up and would be more than a match for the Doctor. It would be a great coup to get her."
Lady GaGa recently ordered ghostbusters to get rid of 'evil spirits' on tour.
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