The ICC said as the investigation remains ongoing and nobody has been charged with any offense, no further comment will be made by either the ICC and NZC.
NZC chief executive David White said his organization was aware the ICC "is investigating some former New Zealand cricketers."
He said only a "small number" of players were involved.
"It's a difficult situation," White said. "Unfortunately, we are not in a position to comment further and all inquiries have to be directed to the ICC."
The Herald report said the ICC investigation was focused on "historic matches involving international stars." It said the probe "has concentrated on cricket at a domestic or franchise level" and it was not known whether it would reveal any attempt to fix international matches.
The newspaper said none of the New Zealand players involved was still playing professionally.
The New Zealand government last week announced measures to combat drug taking, match fixing and the involvement of organized crime in sport, including the introduction of new laws which will make fixing a criminal offense. Those laws have yet to be enacted.
Former New Zealand test allrounder Jacob Oram, who played for several season in the Indian Premier League, said he is surprised New Zealanders are under investigation.
"In a way it's disappointing to think that if it does come out as correct that New Zealand is involved and potentially heavily involved in it...that's disappointing for New Zealand's reputation around the world," he told LiveSport Radio.
"I just hope it's not...one of our greats or three of our greats and then everything you thought you know, your world would just get turned upside down."
During an undercover investigation last year by Britain's Sunday Times, leading Indian bookmaker Vicky Seth told a reporter he had contact with New Zealand players.
"At the moment we've got connections with New Zealanders," Seth said.
He named two players whom he claimed to have met in Delhi in 2010 but the names have not been published.