NSW Health Minister Brad Hazzard is looking at ways to require all health workers to be vaccinated, the ABC understands.
It comes on the back of the Liverpool Hospital cluster, which has seen at least two partially vaccinated nursing staff contract the virus.
Five patients at Liverpool Hospital have now died as a result of the outbreak.
Health staff, including students and those who deliver meals to wards, are already required to be vaccinated for a variety of diseases, including hepatitis B and chickenpox.
But both the Nurses and Midwives Union (NSWNMU) and the Health Service Union (HSU), said a vaccination mandate for COVID-19 was not appropriate and could even lead to staff leaving the industry.
NSW Chair of the Royal Australasian College of Surgeons Payal Mukherjee said both the state and federal governments needed to step in and set high standards for vaccination of health workers, in the same way they were expected to wear PPE.
"I would advocate for the principles of vaccination and that this should be coming from government and certainly the federal government," she said.
"To leave it to individual hospitals creates a high level of stress and variance.
"Without having any vaccination standards, it's just really unfair to expect hospitals to all do the same thing.
"Health care providers work across different hospitals, so it's really confusing."
Dr Mukherjee warned that having unvaccinated health care workers could cause some people to put off medical appointments.
"What you don't want to be doing is create a misperception [that] if you go to hospital, you're at risk," Dr Mukherjee said.
"We were mopping up in September and October all the delayed cancer presentations, so it doesn't do anyone any good."
HSU secretary Gerard Hayes said taking a hardline approach to COVID vaccines would not promote the same cooperation seen around other vaccinations.
"I think those vaccinations have come over time and have been introduced over time and there's been thorough explanations," he said.
"At the moment, things are moving very fast and the information is changing consistently.
"So I think it's just about taking a breath and getting people to come with you."
Mr Hayes said most Australians were generally compliant but when pushed into a position they could be "pretty rebellious and I'm just trying to avoid that".
NSWNMU general secretary Brett Holmes said all other avenues needed to be exhausted before COVID-19 vaccination was made compulsory.
"Let's fix all of the issues around vaccination before we start making the judgement that it requires the removal of choice," he said.
"You need to make sure there has been access, there's been choice, that there's been education."
Mr Holmes said there were still areas across the state where all of those issues had not been addressed.
"There's still people who are on the waiting list or had their vaccination delayed for whatever reason and there are still going to be people that have medical reasons not to be vaccinated."
From mid-September, it will be compulsory for aged care staff to be vaccinated and both Mr Hayes and Mr Holmes expressed concerns some of those workers would quit or retire as a result.
The ABC has contacted the Federal Health Department and both federal and state health ministers for comment.