Doctor Who fans have been left fantasising over the possibility that Peter Jackson may one day direct an episode of their beloved show after he posted a homemade video that included a cameo from the star of the series, Peter Capaldi.

In a video filmed in his New Zealand home with his daughter Katie and posted to Facebook, the Hobbit director teases the notion that the Doctor Who writer and producer Steven Moffat is pestering him to sign up for the gig.

“Hey dad, Steven Moffat’s trying to email you,” Katie says in the video, as Jackson nonchalantly polishes his four Oscars.

“He’s always emailing me,” Jackson responds, in a troll worthy of Middle Earth.

“Put it this way. I reply to the ones I can understand but some are a bit incoherent, you know, like his scripts. I mean, there are great ones and there’s ones that are ... [Jackson pauses for effect] ... not great.”

The Lord of the Rings director says he can’t blame Moffatt. “He’s writing Doctor Who at 10 o’clock; 11 o’clock [he’s] got to do Sherlock; [then he] bangs out an email to Peter Jackson ... can’t even read them half the time.”

In a joke at his own expense, Jackson says he might consider a six-month shoot in New Zealand but not the 12-day production in Cardiff that Moffat is requesting.

Later in the video, the Timelord himself, Peter Capaldi, appears at the door in full costume, with a sealed envelope containing a contract from Moffat and the BBC. The Doctor Who actor has just visited New Zealand as part of a series of fan events.

“I’m the Doctor,” Capaldi says in the video. “Who?” asks Jackson. “Correct,” says Capaldi, in a nod to the perennial schoolyard joke, before being chased out of the room by a Dalek.

The video puts one further tease on the table – literally – in the shape of a bashed-up copy of JRR Tolkien’s book, The Silmarillion, complete with pink Post-it notes.

Fans have long hoped that Jackson might win over the Tolkien estate for the rights to direct a film adaptation of the book.