Investment analysts say a Kiwibank share offering would be embraced by ordinary people in this country who want to invest.
Finance Minister Bill English has suggested there could be a partial float of the state-owned bank if the National Party is re-elected next year.
Investment company Milford Asset Management says demand for Kiwibank shares would outstrip supply if the Government goes ahead with the idea.
It says New Zealanders would be drawn to both the financial security in banking and the homegrown status of the institution.
The Shareholders Association agrees, saying that small investors would be particularly interested if the Government was the majority shareholder.
The Council of Trade Unions, meanwhile, is cautioning that even a partial privatisation would risk changing Kiwibank's purpose.
CTU economist Bill Rosenberg told Morning Report that even a 20% share sale would put the bank's public functions second to profit maximisation.
Australian banks 'taking keen interest'
An analyst in Australia says banks there are taking a keen interest in the debate over Kiwibank's future.
Southern Cross analyst T S Lim in Sydney says Australian banks take an interest in KiwiBank because it makes life difficult for them in New Zealand.
He says a partial float would bolster the bank's resources and potentially double its size.
The bank has an extensive network, Mr Lim says, and with more capital it would prove strong competition for the Australian banks in terms of attracting deposits.
Kiwibank was set up by New Zealand Post as a subsidiary to provide a domestic alternative to the main Australian-owned banks in 2002. It now has assets of $12 billion and 700,000 customers.