Writer Frank Cottrell Boyce, who collaborated with Boyle for the Opening Ceremony for the London 2012 Olympics, told Digital Spy that he wants to write for the series.
"I'm always slightly aggrieved that I never got asked to write for Doctor Who," Boyce said.
"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, Smith said: "Danny Boyle, I would just have a heart attack if he came anywhere near Doctor Who.
"I would love it. I just think he is the most brilliant director. I completely admire his work."
Speaking to DS and other journalists at London Comic Con MCM Expo, Smith added: "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."
Smith continued: "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."
Watch the trailer for the London 2012 Olympic Opening ceremony DVD/Blu-ray box-set below: