The potential airport deal is different from a "right of first refusal" clause included in a 2013 settlement "agreement in principle" fleshed out between Mana Ahuriri and the Crown under which the group would have been able to buy the shares only if the Crown decided to sell.
If the deal does proceed it will be the first time a stake in an airport has changed hands as part of a Treaty of Waitangi settlement.
Mana Ahuriri approached Hawke's Bay Airport last year, asking it to consider changing the airport's name to Ahuriri Airport Hawkes' Bay. The airport company was supportive but asked its two local shareholders, the Napier City Council and Hastings District Council, to formally back the proposal.
Napier, which owns 26 per cent of the company, did so in May, but at a meeting last week, the Hastings council, which owns the other 24 per cent, opted to support a slightly different name not favoured by Mana Ahuriri: Hawke's Bay Airport Ahuriri.
The Hastings decision was slammed by Mana Ahuriri deputy chairman Piri Prentice, who called on the airport company to push on with the original name-change proposal.
Airport chairman Tony Porter said yesterday the company planned to talk with stakeholders before deciding how to proceed on the naming issue.
Mr Prentice could not be reached yesterday, but has previously said if Mana Ahuriri did own part of the airport it would not be interested in onselling it.
Mana Ahuriri will hold nine meetings at venues in the North Island between July 31 and August 17 to outline the details of the deed of settlement and a planned post-settlement governance structure for the group.