US President Barack Obama is "desperate" to come to New Zealand because he has friends in Auckland and his children want to make the trip, Prime Minister John Key says.
But Mr Obama's office is against the idea, Mr Key said this morning, because of the outgoing president's busy schedule in his final year of office.
In an interview with More FM, the Prime Minister also underlined the extensive security required for a visit by a US President, recalling that former president Bill Clinton's movements while in New Zealand in 1999 depended on whether he could be protected by snipers.
A visit by FBI director James Comey to the Beehive yesterday prompted speculation that he was laying the groundwork for an Obama visit.
However, the US Embassy in Wellington said Mr Comey was in New Zealand to discuss "a host of important issues regarding the safety and security of the citizens of both countries".
Any security planning for a presidential visit would be done by the Secret Service, not the FBI.
Mr Key reiterated on More FM this morning that Mr Comey's visit had "nothing to do with Barack Obama".
"If he was coming I would know," he said.
"And I can honestly hand on heart tell you that I don't know."
Mr Obama has expressed his wish to travel to New Zealand privately but also publicly during the Prime Minister's last visit to Washington.
However, the President's office was reluctant to fit a long-distance trip into his hectic schedule, Mr Key said.
Mr Obama's interest in this country was partly because he had friends in Auckland and because his daughters, Malia and Sasha, were "really keen to come".
It has been suggested that Mr Obama could make the trip at the tail end of visits to Asia-Pacific countries, either in April or June.
Any presidential trip was likely to be a costly and complex exercise, Mr Key said.
He recalled that during Clinton's Apec visit, the former president was prevented by his security from going on the Shotover Jet in Queenstown.
Mr Key: "And the reason he wasn't allowed was nothing to do with whether it was safe or not - obviously it is - but because the Americans didn't have enough snipers to put on every half a kilometre of the ridge up the top.
"And people were apparently saying, look, this is New Zealand, you don't need 200 snipers on the ridge over the Shotover River.
"And they said 'Tough luck, sunshine, that's the way we roll. We don't have the snipers so he ain't going on it'."
Mr Obama has never visited New Zealand during his seven years as US President.
US ambassador to New Zealand Mark Gilbert told the Herald in January that Mr Obama had told him personally that he would like to travel to this country.
Mr 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."
Mr Obama's busy schedule is likely to have been complicated further by the death of US Supreme Court judge Antonin Scalia, which means he is tasked with nominating a replacement.