Linton could not elaborate on when the inquiry began or what the process would involve.
An investigation is triggered by the SFO Act, involving formal powers, where the Director has reason to suspect that an investigation into the affairs of any person may disclose serious or complex fraud.
A Waikato District Health Board spokeswoman yesterday said the board was not aware of the preliminary inquiry but would co-operate fully if contacted by the SFO.
On Friday the Herald revealed details of an Audit NZ investigation into Murray's expenses which found he took two international work trips while on sick leave, used public money for personal jaunts, did not declare hospitality, booked travel without approval and tried to cover up the breaches.
The release of the report followed months of Herald revelations about Murray's activity during his time carrying out the $560,000-a-year job, including that he spent more than half his final year out of the office on overseas and domestic trips.
It came as board chairman Bob Simcock admitted DHB failings over the case.
Simcock said Murray charged unauthorised and unjustified expenses to the DHB without his knowledge.
"Unfortunately, the organisation paid those expenses without checking if they had been authorised."
However the Herald reported in August that Simcock first received complaints about Murray being a no-show to an overseas business event as early as March 2015, more than two years before the DHB launched an investigation into Murray's expenses.
Two delegates on a trip to the United States for a conference and site visits, that Murray was supposed to attend, raised concerns with Simcock when the group of 35 New Zealand health professionals returned.
Simcock told the Herald in August he was aware of the trip and thought Murray's programme changed to take in a visit to HealthTap, the American company based near San Francisco which powers the DHB's SmartHealth app.
Murray said he was conducting other business on behalf of the DHB but when his expense receipts and travel request forms were released by the DHB on November 3, it showed he listed Vancouver as one of the destinations he flew to on that trip, which cost taxpayers almost $9000.
The DHB has since reduced the cost of that visit by more than $7000 and billed the rest to Murray after he flew to Canada for a week in the middle of the trip without a valid business reason.
On Saturday, board member Dave Macpherson said he wanted the SFO to investigate Murray's expenses.
Murray paid back $30,000 in May toward the extra money he spent on relocating from Canada to Hamilton in mid-2014, and the DHB said he owed less than $50,000.
However Macpherson said he believed the SFO should investigate based on the number of times the unauthorised spending occurred because it was public money.
"I welcome the inquiry because Nigel Murray's expenses are not all settled."
Representatives for Murray could not be reached for comment.
Criteria for complaint investigation
• Impact – number of people affected and how significantly
• Scale – if it undermines public confidence in New Zealand as a safe place to invest, or undermines the integrity of our financial markets
• Complexity – factual, financial or legal complexity beyond the resources of other enforcement agencies
• Public interest and the preventative impact of a successful prosecution.
