The Government is receiving advice about listing the first state-owned asset up for partial privatisation on the Australian stock exchange.
But Prime Minister John Key says no firm decision has yet been made been made about whether to do this.
The Mixed Ownership Model Bill passed in Parliament by 61 votes to 60 on 26 June this year. The legislation opens the door for the sale of up to 49% of shares in Genesis Energy, Meridian Energy, Mighty River Power and Solid Energy.
The first partial sale will be of Mighty River Power due in September this year, depending on market conditions. The Government's target is to get between 85% and 90% of New Zealand ownership of the company.
Mr Key says some Australian fund managers who act on behalf of New Zealand investors can trade shares only if a company is listed on the Australian stock exchange. He says the Treasury is providing the Government with advice.
However, Mr Key says ultimately, the trading of shares in Mighty River Power will almost certainly be on the New Zealand stock exchange.
Opposition parties Labour and the Greens say listing Mighty River Power in Australia undermines the Government's line that it wants New Zealanders to be first in the queue for the shares.
Labour's Clayton Cosgrove says it will be Australians who benefit if Mighty River is listed across the Tasman.
"Why would you do it - unless you wanted further foreign ownership. It makes it easy for large institutions in Australia to buy in. They have more confidence, because it's listed on their stock exchange.
"And so the Key propaganda and spin unravels again. We were told Kiwi mums and dads would be first in the queue."
Green Party co-leader Russel Norman agrees.
"What we're seeing is a rapid unravelling of the Government propaganda that this is going to be kept for New Zealanders.
"They're clearly facilitating Australian investment in these companies and that will have long-term detrimental impacts on New Zealand's current account deficit as the profits fall overseas and, of course, in terms of New Zealand control of these assets."