Iannucci's Thick of It colleague Peter Capaldi will become the new star of the BBC sci-fi drama from this Christmas onwards.
"I'd love to write [an episode]," the Veep creator told What's On TV. "Steven Moffat hasn't asked me, but it would be great because I love sci-fi and I grew up with Doctor Who as well."
Iannucci added that he was "so pleased" when Capaldi had been cast as Doctor Who's new lead, calling the actor "a massive fan".
"I think some people will be surprised because he's a fantastic actor," he continued.
"He's really funny, so I imagine there'll be lots of humour there, but he can also be powerful and tragic."
Capaldi will make his first appearance as the 12th Doctor in the show's 2013 festive special, which begins shooting this Sunday (September 8).
> Doctor Who writer defends Capaldi casting: 'It's not Made in Chelsea'
Watch Peter Capaldi's unveiling as the new star of Doctor Who below: