Auckland Cricket responded with "No, wait".
If the NZC outcome is successful, ratepayers will field the costs of what has been estimated as a $20-$40 million project budget.
NZC said Auckland was missing international cricket exposure and the subsequent economic benefits due to the lack of a cost-effective, financially-viable venue.
In a March 27 submission to the 2018-2028 Auckland Council long-term plan, NZC chief executive David White wrote:
"Eden Park – the only ICC-sanctioned arena in New Zealand's most populous city, is unaffordable for all but the biggest and, by definition, the rarest of international cricket fixtures.
"Additionally, Eden Park's small size and rectangular, football-shaped playing field continually risks compromising the integrity of cricket matches hosted there.
"Resource consent restrictions and a lack of fan-friendly, cricket-specific features at the arena limits NZC's ability to schedule a greater number of games in the city."
Auckland Cricket chief executive Iain Laxon said they were aware NZC had been talking to the RFA about the possibility.
"We're still in a position where we feel we get great benefits from Eden Park in terms of the facilities and in financial sense.
"Nothing we have seen in terms of an option around Western Springs is suitable for Auckland Cricket's requirements, but we're open to having some conversations."
As an original owner of the Eden Park site, Auckland Cricket's guarantees as part of an existing deal include an approximate $330,000 annuity under the Eden Park Trust Amendment Act 2009. That is further supplemented by cost savings on office space - as tenants at the ground - carparks, and the maintenance and use of the indoor facility.
The annuity would remain regardless of any move; the expenses would need negotiating.
The NZC and RFA positions suggest a shift could occur from what has been Auckland's international cricket home since the New Zealand-England test in February 1930.
Auckland has hosted three tests since 2006, but Eden Park remains International Cricket Council-compliant because it was an established ground before the latest regulations on minimum ground size came into effect.
White said a new 20,000-seat stadium in a natural amphitheatre with grass banking at Western Springs made a lot of sense.
The submission supported flexibility at the venue, with the likes of a drop-in pitch meaning non-cricketing events like concerts could also take place.
Western Springs might have a lower capacity than Eden Park, but the net costs of staging games are expected to be lower because of reduced rental fees.
NZC also proposed shifting to Western Springs as a long-term tenant, as well as the prospect of becoming a high-performance base for servicing professional men's and women's players.
Auckland Cricket was less convinced.
"If you're looking at an international scenario, it's pretty easy to accommodate a drop-in pitch which you can take out and have concerts on," Laxon said.
"But we've got 70-80 days of [Plunket Shield, List A and Twenty20] cricket [each summer] if you include trainings on a field that needs a wicket. That pretty much rules out a multi-purpose stadium.
"If there were two ovals at that site you might be able to work around that."
Such a scenario is not beyond the realms of possibility, given the space available.
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