"It is important for New Zealand that we have as strong a relationship with the US as is possible and I would do everything I can to make sure that relationship was as strong as possible," Little said.
"If it meant meeting with Donald Trump I would do so."
National minister Paula Bennett and Labour deputy leader Annette King each backed Clinton as a woman.
Bennett: "I think it would be great to see a woman in the top job and it would be good for America."
King said: "I want her to win and I want her to be the first woman President of the United States. They are a long way behind New Zealand," she said, referring to the fact New Zealand has had two women Prime Ministers, Jenny Shipley and Helen Clark.
Clinton, a former First Lady, is the favourite to win and would become the first woman US president - but the seventh former Secretary of State.
A win by Trump, a TV celebrity businessman, would represent a huge upset to the established political order and financial markets.
'OUTSTANDING COUNTERPART'
Foreign Minister Murray McCully told the Herald that during the four years Clinton was US Secretary of State, she was "an outstanding counterpart to work with".
"Without getting into US domestic politics, I've only had very good experiences as a consequence of working with her on New Zealand's behalf.
"And I'm sure we'd have good experiences with her again if she was to be elected president."
McCully is preparing for a visit by Clinton's successor, John Kerry, who will touch down in New Zealand on Wednesday - presumably learning the election result on the way - before heading to the Antarctic.
He will return to New Zealand at the weekend for talks on Sunday with McCully and Key.
Defence Minister Gerry Brownlee will meet Kerry en route to the ice.
Kerry and McCully worked closely together on the proposal for the world's largest marine sanctuary in the Ross Sea, which was accepted last month.
COINCIDENCE OF INTERESTS
McCully said the joint proposal was never part of the plan to repair New Zealand's relationship with the United States - which was put on ice for 20 years over New Zealand's anti-nuclear stance.
"This was a coincidence of genuine interests," McCully said.
"This is a part of the globe that New Zealand has a special responsibility for."
New Zealand shared that responsibility with the United States and they had been treaty partners there for over 50 years.
There was a high degree of interdependence between New Zealand's Scott Base and the United States' McMurdo Station.
"We just think about that part of the world in partnership terms. That's how it is for us."
