Speaking to Digital Spy and other journalists, the director explained that discussions about his involvement are "actually kind of serious".
"I would be very happy to," Jackson said. "I'd love to try my hand at television, because I've never had the discipline of having to shoot for those impossibly tiny schedules. I think I could do it okay now."
The director went on to joke that the prospective episode might be shot on location, given his own reluctance to work outside of his native New Zealand.
"I did suggest that they did a New Zealand story - something to do with the [rugby union] All Blacks versus the Daleks. There's a good story in there, although obviously the All Blacks would have to win!"
Doctor Who's former executive producer Caroline Skinner has previously said that she would "love to bring Doctor Who down under" after the show's 50th anniversary episode, which aired last month.
Jackson's second Hobbit film The Desolation of Smaug is released this Friday (December 13). Watch a trailer below: