The couple - who welcomed their first son, Flynn, into the world in January - were spotted looking at a four-bedroom rental property on the island yesterday (23.08.11).
According to website JustJared.com, the house also boasts a gym, home cinema, spa, swimming pool and wine cellar.
Orlando and Miranda usually divide their time between Los Angeles and London, but the couple could be looking for a long-term base while the British actor films the two forthcoming 'Hobbit' movies on the island, which is situated 1500km away from his spouse's native Australia.
Earlier this year, Orlando spoke of how he finds Los Angeles can be overwhelming.
He said: "My first overriding memory of LA is flying out of the city to New Zealand to do 'Lord Of The Rings' and looking out of the window of the plane thinking it looked big and intimidating.
"A bit scary really - just so vast and bustling."
The 34-year-old star has also spoken of his desire to raise his son without being in the public eye too much.
He said: "It's good in LA but I kind of live in London as well. Most of the time I keep it very quiet as I like to be at home and not in the eye of it all.
"You can't avoid it sometimes in LA unfortunately - I try my best but it's very difficult.
"When I'm in the UK, and I'm here more than people would think, I tend to keep a very low profile. I just enjoy being home with my family and mates and stuff."