Infratil went into a trading halt on Friday morning after it made an announcement to the New Zealand stock exchange, confirming the talks.
It said the halt in trading would last until it could make an announcement about the acquisition or the opening of the NZ market on Tuesday (14 May), whichever was earlier.
"Following recent media speculation, Infratil confirms that it and another party are in discussions with Vodafone Group Plc (Vodafone) regarding a potential transaction involving an acquisition of Vodafone New Zealand," Infratil said in its statement to the exchange.
The Australian Financial Review claimed it had been first to report the discussions and said the unnamed company was Canadian fund manager Brookfield. It put the value of the deal at $2.5 billion.
Trans Tasman infrastructure investor Morrison & Co manages Infratil. Vodafone New Zealand is owned by the Vodafone Group.
Contacted for comment, Vodafone New Zealand told iTWire that it had no comment on the acquisition attempt.
The news of the proposed acquisition of Vodafone New Zealand comes a couple of days after the Australian Competition and Consumer Commission refused to give the green light to a proposed merger between Vodafone Hutchison Australia, which is half-owned by the Vodafone Group, and TPG Telecom.