Association of Salaried Medical Specialists executive director Ian Powell called on Simcock to resign if Murray was found to have inappropriately spent taxpayer money.
"If these claims are found to be correct, ie inappropriate use of expenses, then I don't think Mr Simcock has any choice but to resign."
Powell said senior doctor representatives met Simcock before Murray's appointment in 2014 to express concerns.
Waikato-based Labour MP Sue Moroney said she also met with Simcock to raise concerns about Murray's history in New Zealand's health sector.
Shortly after, a Canadian Government review showed Fraser Health Authority in British Columbia, where Murray resigned early, was underfunded.
Board member Dave Macpherson this week questioned Simcock over his governance. As chairman, Simcock must sign off the chief executive's expenses.
"I've asked Bob a series of questions about who authorised this, and if it wasn't him how did it get paid if it wasn't authorised?"
He asked whether Simcock's actions or lack of would be part of the investigation and if there were over-payments in the expenses.
Simcock told the Herald an Auckland barrister was undertaking the investigation into all of Murray's expenses since July 2014 and an employment lawyer was overseeing the process.
Audit New Zealand was also conducting an audit of the DHB's management of the process, including the authorisation and payment of the expenses, he said.
The expenses include Murray's $36,000 relocation costs from Canada.
Simcock said Powell and Moroney's concerns were about their experience with Murray as the lead negotiator for New Zealand DHBs during a "bitter" wage negotiation and were not relevant to the current situation.
In response to Powell's claims that he should stand down if inappropriate spending was found, Simcock said he had not considered it.
He undertook exhaustive reference checks of Murray at Auckland DHB, Southern DHB and Fraser Health Authority and all were "strongly supportive" of Murray.
Simcock did not recall Fraser Health raising issue with Murray's expenses there, $140,000 over an 18-month period.
Murray left Southern DHB in 2007 to be chief executive at Fraser Health and was later cleared of breaching his employment contract by carrying out consultancy work for Fraser Health while he was still the chief executive of Southern DHB.
Simcock said the investigation could last another three weeks and at this stage Murray was due back from extended leave on August 23.
Once concluded a report on the investigation would be heard by the board's remuneration committee, in public excluded.
Simcock said it was disappointing "to get involved in a process like this" but his views about it would be determined by the outcome.
He added it was too early to determine Murray's future at the DHB.
This is not the first time Simcock has been in governance roles of organisations which have come under scrutiny.
He was Hamilton mayor when the city hosted the Hamilton V8s and a PwC review carried out into the event found he was involved in keeping financial problems about the V8s from councillors for two years and criticised his council for having too many meetings behind closed doors.
The council's management team was reported to have spent millions of dollars without authorisation and kept council in the dark over significant issues.
Simcock was also on the board of Karapiro 2010 Ltd which was the organisation set up to run the 2010 World Rowing Champs.
A SPARC (Sport and Recreation New Zealand) review into the event following a budget blowout was highly critical of its board, saying there was a lack of clarity around its role and responsibilities, and poor financial monitoring.
In response to questions about whether he was reviewing Simcock's role as chairman, Minister of Health Dr Jonathan Coleman said in a statement Simcock was appointed chairman of Waikato DHB following a process based on State Services Commission guidelines.
