Thirty-nine people are seeking the position of chief executive of the Southern District Health Board.
Mr Butterfield said the application date had passed but a few more applications might be received soon.
"We are pleased with the high calibre of applicants," he said.
It was hoped a shortlist could be presented to the board at its meeting in November.
The next steps included detailing the background experience of the candidates; and preliminary interviews.
Mr Rousseau, whose salary is between $490,000 and $500,000 a year, leaves the board in the middle of this month.
The existing deputy chief executive, Lexie O'Shea, who is the chief operating officer at Southland Hospital, will take over the role until the new appointment.
