Economic development minister Simon Bridges said should the team win the battle in Bermuda, they expected Team NZ will want to discuss with the Government what a future partnership may look like.
"However, for now, it would be premature for the Government to consider potential investment in Team New Zealand's next America's Cup campaign before we can fully understand the opportunity that the next event holds for New Zealand and New Zealanders.''
A spokeswoman for Labour's Sport and Recreation spokesman, Trevor Mallard, also said he thought any discussion of support was premature.
"Let's win the damn thing first,'' he said.
ACT's leader and sole MP, David Seymour, would not be swayed to give taxpayer funds to the next campaign - even if the Kiwis brought the Cup back home this time around.
"It is not the Government's job to fund yacht races. That would be corporate welfare - which ACT opposes."
In 2013, the Government put $36 million of public money towards the America's Cup Kiwi campaign, but has not contributed to the Bermuda campaign.
If New Zealand was to win hosting rights at some point, Seymour said those who should be forking out for the costs were private sponsors.
"If there are profits to be made from hosting the Cup here, then the businesses set to collect those profits can sponsor the event."
Co-leader for the Greens, James Shaw, reiterated ACT's stance, saying: "Frankly, I think the Green Party has got higher priorities than funding an elite sport like this.
"We're dead against corporate welfare and subsidies, but if there's a case to be made for the Government co-investing, then the business case needs to be absolutely rock solid."
Total transparency was needed if it was decided public money would be invested into Team New Zealand, he said, as taxpayers had the right to know exactly how their money was being spent.
"I'm still not clear why public money has to be co-invested. That, to me, is the critical question. Because if it's that good a deal, surely the private sector can fund it fully."
NZ First's Clayton Mitchell acknowledged the party had supported the campaign in 2003, but said they had yet to discuss the subject this time around.
"I think it's a great event...but we as a caucus decide. Certainly, if it was going to bring wealth and opportunity and GDP growth for the economy, then that would certainly, I'm sure, have a positive effect on the decision being made by our caucus."
Maori Party co-leader Te Ururoa Flavell ruled out his party supporting any future public funding of the syndicate.
"While it's all well and good to back the team and be proud of their efforts whatever the outcome, we simply can't see how funding for the hosting of a boat race should take priority over putting people into warm, safe, affordable homes," he said.
Meanwhile, Ateed general visitor and external relations manager Steve Armitage said the Auckland Council-funded body said it was also too soon to say what financial backing it would give a potential Auckland defence if Team New Zealand was successful.
Armitage said it had been "fantastic" to see the syndicate excelling on the way to the America's Cup final.
Auckland had proven itself as a host of major sporting events in the past, but he said any decisions about Auckland being a host city of a future America's Cup or related event would need to be in partnership with central government and the private sector, "in order to maximise the economic return opportunity and deliver a world-class event".
"It would also be contingent on a New Zealand cup defender's decisions about competition format, host country and host port," he said.
"But, from last experience, it's probably best to wait until the last race has been sailed and the defender of the next America's Cup is confirmed."
