Mr Key believes resuming ship visits would be a positive step and extend markedly improved relations between the nations - and a new poll shows 75% of New Zealanders agree.
The Navy has invited the US Navy, among others in the world, to its 75th birthday celebrations in November and the Pentagon is considering it.
But an acceptance would run counter to the most significant remaining reprisal against New Zealand's anti-nuclear laws.
The US Navy has boycotted NZ ports since 1986 when New Zealand was effectively expelled from the Anzus security pact with the US and Australia.
Reprisals have eased only in recent years. The ban on the US exercising with NZ was lifted only in 2010. But even then the Kiwis were not allowed to dock in naval facilities at Pearl Harbour but had to dock at a civilian wharf. President Barack Obama overturned that particular oddity for the 2014 Rimpac exercise.
Under New Zealand law, ships may visit only if the Prime Minister is satisfied they are not carrying nuclear weapons.
It does not require any confirmation that a ship is not nuclear armed. US ambassador Mark Gilbert has said the US would not relax its long-running policy to refuse to confirm or deny if a Navy ship was carrying nuclear weapons.
Mr Key, talking to Newshub this morning, indicated that obstacle could be overcome, and he could accept the advice of Ministry of Foreign Affairs and Trade (Mfat), without the need for a US confirmation.
"I have to sign a waiver, which I get from foreign affairs to say they meet our New Zealand anti-nuclear law - in other words, it is neither nuclear-powered or carries nuclear arms. How they decide that I don't know, but they'll have a way of going through it."
According to a new Newshub Reid Research poll, 75% of respondents supported a US Navy ship visit. Twenty per cent were opposed, and 5% did not know.
In January, the results of a Herald DigiPoll showed a total of 29.4% didn't want a ship to visit at all; 50.2% think it would be a positive move; and 16% displayed a sense of triumphalism by preferring to think it would be a victory for New Zealand's anti-nuclear policy.
