A Wellington Free Ambulance spokeswoman told the Herald they were called to the Newtown property last night, and that the man was in a "serious" condition on arrival.
The owner of the lodge believes the man, who has been unwell for "years", suffered a heart attack.
It is understood the man was aged in his 40s, had a high fever, and was suffering from recent coughing and breathing issues, Stuff reported.
But lodge owner Matthew Wright said the man was a "very large" person who had suffered from health issues for some years.
He had been living at the lodge for about four years and as far as Wright knew had not been in contact with any known coronavirus cases.
Wright said the lodge was not a "tourist type operation" and had a minimum stay period of 28 days, with most guests staying for between one and 10 years.
He was unaware of any of their guests having travelled overseas recently or being in contact with people who had coronavirus.
Wright said the man had been in hospital recently and discharged himself.
A Ministry of Health spokesman declined to confirm whether the case was being treated as a potential coronavirus case, saying only that updates on Covid-19 would be provided at the 1pm press conference.
Bloomfield said during the conference there was no suggestion he died of a Covid-19-related transmission.
He said anyone delaying seeking treatment for other illnesses shouldn't and should still call their GPs to organise an appointment.
"Please do not delay seeking treatment for any medical need you might have."
There are currently 1039 confirmed cases of coronavirus in New Zealand, and one confirmed death.
West Coast woman Anne Guenole died a week ago after being admitted to hospital with flu-like symptoms. The 73-year-old tested positive for the virus shortly before her death.