Tuffey initially said he was in the dark and shocked by the allegations of his involvement. He released a statement through his lawyers at the weekend about the investigation.
The International Cricket Council anti-corruption panel is believed to be looking at matches involving New Zealand players that took place in India, South Africa and England, raising the possibility that criminal charges could follow if any are found guilty.
The players named are Tuffey, Cairns and Lou Vincent.
Tuffey did not respond to messages from the Herald.
But a statement released to media by his lawyers said: "Mr Tuffey does not believe he is the focus of this investigation. He intends to fully co-operate with the ICC and provide them with any relevant information in his possession. He will not be making any further public statements at this time."
Tuffey's admission follows Vincent's confirmation that he was talking to the ICC in relation to an investigation into match-fixing.
Cairns has steadfastly denied any involvement and said to have his name linked with the scandal was "sickening".
In a column in a Sunday newspaper, he maintained his innocence, despite "rumour and press speculation" around the world.
"As I pen this article, no-one from the International Cricket Council or NZ Cricket has approached me about this investigation. Yet I am named around the world as one of three New Zealand cricket players involved in it."
The ICC has refused to be drawn on the specifics of the allegations. They alleged that a "small number of former New Zealand cricketers had engaged in fixing activity in historic cricket matches".
"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."
It said it had a zero-tolerance attitude towards corruption in the sport, and the ACSU would continue to collaborate with relevant individuals in order to complete its investigation.
