In a media statement on Thursday, ICC said they have been investigating match-fixing allegations over the past few months. However, they did not name the players.
A report in "New Zealand Herald" said Cairns, Tuffey and Vincent were the players under probe.
"Following the publication of an article in a leading New Zealand newspaper earlier today in which it is alleged that a small number of former New Zealand cricketers had engaged in fixing activity in historic cricket matches and were being investigated by the ICC's Anti-Corruption and Security Unit (ACSU), the ICC confirms that it has indeed been working closely over the past few months with its colleagues in the domestic anti-corruption units of Member Boards to investigate these and related matters," ICC said.
"The ICC and all of its Members maintain a zero-tolerance attitude towards corruption in the sport, and the ACSU will continue to collaborate with relevant individuals in order to complete its investigation process.
Naturally, as the investigation remains ongoing and nobody has been charged with any offence, no further comment will be made by the ICC or by NZC," ICC added.
Reacting to the news, Cairns was quoted as saying, "We need to let the investigation by the ICC run its course."
Vincent said: "I wish to let everyone know that I am cooperating with an ongoing ICC Anti-Corruption investigation that has been made public today."
"This investigation is bound by a number of rules and regulations that mean I am unable to make any further public comment.
"I will personally talk to the public when I am able to. In the meantime I cannot comment. Please respect me and my family's privacy until such time," he added in the newspaper report.