The search started in February, when it was announced acting chief executive Ruth Kibble’s secondment would end in June.
It was hoped the post at Oamaru Hospital would be filled by the end of April.
Mr Paul Allison said the board had advised hospital staff of the situation.
"It hasn’t progressed as quickly as we would have liked because of the circumstances. We are hoping that will be finalised in the next few weeks."
He said there had been at least 10 applications for role, both from within New Zealand and from overseas.
The board of the Waitaki District Council-controlled organisation was provided with a long-list of applicants Mr Allison said the company’s recruitment provider "felt were suitable", then that list was whittled down and initial interviews held.
Asked if discussions had been held with Mrs Kibble about possibly staying on to ease the transition to a new chief executive, Mr Allison said that had not been addressed.
"That will be determined by who the successful applicant is and what stage they can start."