Mr Rousseau's resignation was announced this week after more than eight years with Otago, Southland and Southern boards, but he will not leave the job until the end of the year.
However, he pointed out chairman Joe Butterfield could have other ideas.
Mr Butterfield will lead the process, but is in the United Kingdom and not expected to return until early July.
Mr Menzies said the job was a huge one and there were not many people about with the ability and desire to do it.
Mr Menzies said his previous experience with such processes suggested it would involve a minimum of three months to complete the process.
Asked if the remuneration offered was likely to be the same as Mr Rousseau's salary, which is in the $490,000 to $500,000 bracket, Mr Menzies said the board would consult the State Services Commission which set such salary bands.
He expected this would be one of many issues the appointments and remuneration advisory committee, comprising Mr Butterfield (as chairman), himself and board member Richard Thomson, would be considering.
The job description for the chief executive was likely to be "pretty much the same" as that for Mr Rousseau, although the "crucial" key performance indicators for the role would be looked at.
Mr Rousseau was in Christchurch yesterday and could not be reached, but his support manager, Cherie Wells, advised he had received many messages from within and outside the organisation since Tuesday's announcement, which was "heartening".
Dean of the University of Otago's Dunedin School of Medicine Dr John Adams yesterday said he had appreciated Mr Rousseau's acknowledgement of the crucial nature to both organisations of the relationship between the school and the public health service which extended back more than 130 years.
Mr Rousseau had been committed to providing the best health services possible for Otago and Southland and to continue to do that had seen through some significant changes.
"I respect his leadership and clear and innovative thinking."
Wishing Mr Rousseau well, Dr Adams said he had enjoyed working with him for more than eight years, and considered the school and region had been lucky to have him.
