Could Peter Jackson direct a future episode of Doctor Who?

It appears that both Doctor Who's Matt Smith (who currently plays the Eleventh Doctor on the British sci-fi show) and Peter Jackson (The Lord of the Rings, The Hobbit) himself would love to see Jackson's involvement in a future episode of Doctor Who.

While talking to The Waikato Times, Matt mentioned that he would love to film an episode of Doctor Who over in New Zealand. He went on to comment:

"Let's get Peter Jackson to direct one and go and make it in New Zealand. I would love to, I will campaign endlessly to come over and film there."

Now this could be taken as an actor voicing his desire for a exotic location shoot but then The Waikato Times got a hold of Peter Jackson and spoke to him about the matter. Jackson had this to say:

"I'm a huge Dr Who fan, and I think Matt's fantastic. Just name a time and place, and I'll be there!"

Smith and Jackson had a chance to meet recently at San Diego Comic Con where Jackson admitted to Smith that he was a fan of the show. Jackson is even currently working with Sylvester McCoy who was the Seventh Doctor on Doctor Who in the late 80's.

With all of this info do you think (BBC permitting) that we could possibly see Peter Jackson direct an episode of Doctor Who in the future?If so, what kind of episode do you think Jackson should do? Something along the lines of a Middle Earth setting? (We've seen a The Lion, The Witch, and The Wardrobe episode so why not a Lord of the Rings one?) Or maybe go into Jackson's deep past and pull out a classic gruesome horror story? Let me know what you would like to see in the comments!

Source: The Waikato Times