"This needs to have a 30- to 50-year view," she told the Herald on Sunday.
"These are large amounts of cash and I would be really reluctant to go out there and support one venue in one location with such a huge amount of money without seeing the wider strategy for Auckland at an economic development, at a tourism, at a sporting level."
Kaye said the concept of building a stadium in Auckland's CBD had been a divisive one and the proposed strategy would create a domino effect as it would also change where motorsport and cricket were hosted.
She was also concerned about the shortage of community sport facilities across Auckland.
Kaye and Minister for Sport and Recreation Grant Robertson have scheduled a meeting to discuss proposed changes to sporting venues in a couple of weeks.
"I'm very keen to have that discussion - and open minded actually - about where various stadiums should be, but we've also got to make sure that we do the bread-and-butter of kids' sport as well in time," said Kaye.
"I'll be asking how can we work together to make sure we get that long-term view."
Goff on Friday said he had spoken with Robertson about planning for the new stadium but acknowledged both politicians had more pressing priorities at present.
Robertson told the Herald although he agreed he and Goff had higher priorities, he looked forward to having ongoing discussions with Goff about developing sport facilities in Auckland.
Meanwhile, an Auckland councillor has lambasted the proposal, calling it a "mayoral vanity project".
John Watson, who represents the Albany ward, said the city didn't need a new stadium, couldn't afford one and would rarely be able to fill it.
"The stadium debate was had back in 2009 and now we seem to see these consistent attempts to resurrect these grandiose plans at a time when Auckland's got other priorities and when, ironically enough, our existing stadiums have had huge investments of capital put into them in the interim," he said.
The study itself cost $932,000, which Watson said was wasteful considering community sports facilities in South Auckland and the North Shore were in disrepair.
"I think this should be opened up to the Auckland public. People should be informed of the cost and should have a chance to have a say," he said.
New Zealand Rugby chief rugby officer Nigel Cass said the organisation supported Regional Facilities Auckland's venue development strategy.
"Auckland – as New Zealand's biggest city – is important to rugby," he said.
"We are very aware that fan expectations are changing and we need to keep improving that experience to stay relevant and engage current and new fans."
Any shake-up of sport venues needed to consider the changing nature of different codes, competitions and formats, Cass said.
Auckland Blues chief executive Michael Redman reiterated comments made by the franchise during 2016 when a waterfront stadium was proposed for a second time.
"In principle, the Blues support the concept of a new CBD stadium for Auckland and the club would seriously consider any proposal presented to us to become a core user," he said.
The Blues had been consulted for the feasibility study, a spokesman confirmed.
