On Sunday, Mr Key renewed his call for All Black captain Richie McCaw to be knighted for leading New Zealand to two World Cup victories.
He did not plan to speak to McCaw about the nomination, and he said it was up to officials to consider whether the veteran All Black was deserving of a knighthood.
McCaw turned down a knighthood after New Zealand's World Cup win in 2011.
Labour's deputy leader Annette King agreed that McCaw was deserving of the honour, along with All Black coach Steve Hansen and possibly others.
"A quarter of the team came out of the Rongotai electorate," the Rongotai MP said. "I'm talking about Ma'a Nonu and Dane Coles and Julian Savea and I could go through the list."
Ms King reiterated that Labour had not thought about whether it would retain or remove knights and dames if it was in power.
She personally did not want the system to be "chopped and changed" with every change of government. She said greater emphasis should be placed on the Order of Merit, which was unique to New Zealand.
Ms King was also asked about whether the All Blacks and the World Cup had been over-politicised.
She disagreed, saying most New Zealanders were reflecting in the team's glory and it was normal for MPs to want to be associated with success.
The Prime Minister has been photographed several times in the New Zealand side's changing room after each of the knockout rounds of the cup.
Ms King admitted she had once been invited into the British Lions' dressing room at Athletic Park.
"It was a terrible experience," she laughed. "The smell, to start with, [and] liniment and half-dressed men."
The All Blacks will take part in several celebratory parades around New Zealand after returning from England this week, coinciding with a royal visit by Prince Charles and Camilla.
Mr Key hinted that the royals' itinerary could be changed to allow them to take part in one of the parades, possibly in Wellington.
"There's one potential possibility but we're not sure," he said.
Mr Key has also sent an All Black tie to Mr Turnbull as part of a wager the two leaders had on the World Cup Final.
The Australian Prime Minister was expected to wear the tie at parliamentary question time this week.