Writer Frank Cottrell Boyce, who worked with Danny Boyle for the London 2012 Olympics Opening Ceremony, said that he wants to write for the series.
Frank Cottrell Boyce said: "I'm always slightly aggrieved that I never got asked to write for Doctor Who. That's in the same league [as the Olympics]. I'd jump at that."
Asked how he would feel about Boyce and Boyle reuniting to work on Doctor Who, Matt Smith said: "Danny Boyle, I would just have a heart attack if he came anywhere near Doctor Who.
He added: "I would love it. I just think he is the most brilliant director. I completely admire his work. Everything he does. He adds pace, style - whether it's zombies or a guy riding a bike on the way to a cliff or a guy running down a street getting hit by a car.
"I think he's just a brilliantly stylist and the DP [director of photography] that he uses Anthony Dod Mantle is wonderful as well.
"He's one of my favourite filmmakers around. He'd be an amazing director for Doctor Who, but I don't think we'd get him."
"I'd tell you who I'd also think would be great. Edgar Wright. He'd do something brilliant. I think he'd do something really, really clever with it.
"But we're very lucky to have Steven [Moffat]. I count him in that bracket. I think he's a genius."
Would you like to see Danny Boyle and Frank Cottrell Boyce direct an episode of Doctor Who?