The young actress worked with current Time Lord Peter Capaldi on the latest series of the sci-fi TV show, and he is expected to vacate the role next year (17) when lead writer and executive producer Steven Moffat steps down.
Maisie believes the show would benefit from a shake-up after Peter leaves, and she is convinced Luther star Idris would be a good choice to lead the cast.
"I think a black doctor would be incredible. I'm all for Idris Elba," she tells the London Evening Standard.
However, Maisie is also adamant producers should consider giving the traditionally male lead role to a woman.
"I think a female doctor would be incredible," she adds, and admits she would take on the part herself if Idris is too busy: "If (Idris can't do it) I'll take it for the team and do it!"
The Thick of It star Peter made his debut as Doctor Who in season eight in 2014, taking over from Matt Smith, and he will return for season 10 this year (16).
Idris has previously been linked to another iconic British role, James Bond, amid speculation current 007 Daniel Craig is to walk away from the action franchise, but he dismissed the gossip and declared he had become frustrated with the furore.
"I don't even want to answer," he told Britain's The Times Magazine. "There is no point, you know. There is nothing to say. I have nothing to say on Bond. I sometimes slip into a conversation about it and I get quoted again and it looks like I'm always talking about it. I'm over it."
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