With the Kiwi team's immediate thoughts since returning from Bermuda being on negotiating the Protocol and planning their Cup defence, Shoebridge said they are yet to make a decision on what to do with their radical wingsail catamaran.
"We'll consider a range of things. We'll try hold on to it if we can - it's a pretty iconic piece of equipment now, so we'll have to come up with something that is appropriate for it."
Team NZ boss Grant Dalton suggested the Aotearoa could be displayed at the Maritime Museum alongside the syndicate's other famous piece of machinery - the 1995 America's Cup winning boat, NZL32.
He said both boats are considered a shining monument to the capabilities of the New Zealand marine industry.
"In a perfect world we'd like to put it in a museum, but we haven't done anything about that at the moment," he said.
"We haven't had any approaches for that, and we haven't approached anyone either because we've been so focused on the Protocol."
Dalton yesterday confirmed the next America's Cup will be sailed in 75-ft high performance monohulls, but the full class rule will not be revealed until November 30. He believes the return to monohulls will lead to more quality challengers entering the next event, as people within the sport relate better to monohulls.
Auckland is not yet the confirmed host city - Dalton says it will be held in Italy if the city does not ensure appropriate infrastructure.
Economic Development Minister Simon Bridges would not comment yesterday because the Government is in caretaker mode, which means it cannot make any commitments around funding or policies.
The Ministry of Business, Innovation and Employment's general manager of tourism, sectors, regions and cities Iain Cossar said the Government was working closely with Auckland Council to understand the requirements for hosting the event.
Any Government funding in the event would be informed by a business case, he said, and would depend on its ability to promote New Zealand to the world and provide leverage to businesses.
"Any government investment in the event needs to stack up commercially for Emirates Team New Zealand and economically for the New Zealand ratepayers and taxpayers," Cossar said.
NZ First leader Winston Peters and Labour leader Jacinda Ardern did not return calls.