Gilbert said despite the popular belief that a president's mandate waned in their final year, Obama still had "much to get done" in 2016.
"So although the President doesn't have much daylight in his calendar, I'm sure if he can make a visit to New Zealand happen, he would like to."
The ambassador said preparing for a presidential visit was an enormous and complex task, which was often beset by unexpected events.
But New Zealand did have one advantage. Gilbert said Prime Minister John Key's close relationship with the President could be a factor in getting him to travel to this country.
"And I'm sure he will be flattered by the results of your poll as well," Gilbert said.
If Obama were to come to these shores, it would be the first US presidential visit since Bill Clinton's trip for Apec in 1999.
The last Pope to visit New Zealand - which has around 500,000 practising Catholics - was John Paul in 1986. Governor-General Sir Jerry Mateparae extended an invitation to Pope Francis when he met him in Rome in 2014.
Asked which location in New Zealand an important visitor like Obama could not miss, more than a third of people voted for Queenstown.
Abel Tasman National Park, known for its golden beaches and turqouise-coloured water, came second with 25 per cent.
Destination Queenstown chief executive Graham Budd said the South Island resort town had a level of sophistication which VIPs expected when they travelled. "The quality of the accommodation and service and food is, I think, world class," he said.
Dudd said visiting dignitaries and celebrities usually chose to stay at one of Queenstown's luxury lodges, which can charge up to $20,000 a night, and took a helicopter tour of the region.
They also usually visited wine country in Central Otago and indulged in some adventure tourism, such as the Shotover Jet.
Gilbert said it would be too difficult to pick a single place to take Obama in New Zealand. "I'm sure that wherever these meetings with the President might happen, it will be in a beautiful setting."
