The Health Minister has written to the chair of the troubled Counties Manukau District Health Board about his position.
Rabin Rabindran only took over the top job this year.
Middlemore Hospital is at the centre of a political storm over who knew what and when about its rotting buildings.
Health Minister David Clark said in a statement he had also written to one other unnamed board member about their position.
"I have provided them with the opportunity to make any submissions before I make my final decision," he said.
"While that process is underway it would be inappropriate to make any further comment."
Mr Rabindran did not respond to RNZ's calls.
He has refused to give an interview since RNZ broke the story of the rotting hospital three weeks ago.
Mr Rabindran took over the chair from Lester Levy.
Mr Levy had warned in early 2017 of a financial crisis looming.
This was despite Counties Manukau getting top ratings from Treasury, both for "repairs and maintenance" in 2016-17, and overall - it was the only DHB to get a top mark from Treasury for all key performance indicators for 2015.