Auckland City Hospital already has more patients than its 12 negative pressure rooms designed to help prevent diseases spreading through ventilation systems.
RNZ asked the hospital what its plans were once the rooms were full, but it has not yet provided an answer.
All the country's hospitals have been preparing for cases since the Delta variant entered the community, particularly if there is a large surge.
Preparations include how they will rearrange staff, wards and other resources if they get too many cases to cope in the normal set up.
Most are hoping that level 4 restrictions will prevent them being needed.
Intensive Care Society spokesman Andrew Stapleton said if negative pressure rooms filled up, some hospitals would opt to create larger negative pressure spaces and, if they filled up, well-ventilated ward spaces for Covid patients away from others.
College of Anaesthetists president Vanessa Beavis said one contingency was for anaesthetists - many of whom have crossover skills - to step into intensive care if needed.
Theatre nurses were undergoing training now in case they needed to step in to provide intensive care cover, she said.
RNZ understands many doctors and nurses at Middlemore and Auckland hospitals are anxious about the current patient numbers.
Middlemore would not comment on the situation there but in the past its chief executive Margie Apa has said the hospital was well practised in dealing with infectious diseases, caring for hundreds of measles patients in 2019.
Stapleton said hospitals would cope well with the current Covid numbers - most had many more during the RSV outbreak - and patients would receive good care.
Both doctors urged people to get vaccinated as soon as they could, saying that was ultimately the best way to prevent hospitals from being overrun.
Vaccinated people were massively less likely to need hospital-level care.