An immunology expert says people who have not been infected by COVID-19 should receive the vaccine first.
Research suggests people who have previously had the virus are highly unlikely to contract it again.
The University of Oxford study found the disease offers protection from re-infection for at least six months.
Nursing home residents are due to begin receiving vaccines tomorrow, with the Minister for Health saying that all residents and staff will receive their first dose by the end of January.
Trinity College Dublin Immunology Professor Kingston Mills said the rollout of the programme can be expedited if people who have already been infected are eliminated.
Speaking to Seán Defoe on On the Record with Gavan Reilly, he said people who have already had the virus can be identified through documented positive PCR test results or antibody tests.
"There are significant numbers that have been infected, 100,000 is the official statistic in the country but it's vastly more," he said.
"In the healthcare system and in the nursing homes it's certainly over 20%."
Professor Mills said the research from Oxford was "very good news" as the number of people who become reinfected with the virus is very low.
"The bottom line is it means someone who has been infected and recovered doesn't really need to get the vaccine as a priority over someone who has never had the virus," he stated.
"In my view, we should be prioritising people who haven't been infected over those who have.
He added that this would be a preferable approach to giving more people the first dose of the jab by delaying second doses, as suggested in the UK.
The immune response from vulnerable or elderly people to the vaccine is not as strong and therefore giving one dose and delaying the second would not be wise, he said.
On the same programme, the Minister for the Environment Eamon Ryan said 17,000 frontline healthcare workers in hospitals will receive the vaccine next week.
He said as soon as the vaccines are delivered into the country, they will be deployed with no stockpiling taking place.
However, the roll-out will not be 9 to 5, Monday to Friday, he said, despite the HSE previously indicating it would only be administered on that basis.
"Far from it being 9 to 5 or five days a week, it's going to have to be 24/7 in my mind with all hands on deck," he said.
"There's 1,700 people already been deployed, been trained up so there's no shortage of resources, there will be no shortage of impetus to get this out.
"It's in all our interests to get it delivered to as many people as quickly as possible and as safely as possible."