Cork is one of four counties now under consideration for additional lockdown measures following the country's highest daily Covid figures since April.
Health minister Stephen Donnelly confirmed additional restrictions could be announced this week for Cork, Wicklow, Galway, and Louth.
His announcement comes as a worrying 430 new cases of Covid-19 were reported on Sunday, with the country continuing to battle the early stages of a second wave.
The total number of new cases over the weekend was 678, with five deaths reported on Saturday.
Of the 430 cases announced yesterday, 212 are in Dublin, 54 in Cork, 23 in Donegal, with the rest spread across a number of counties. Some 72% of the cases have been found in people under 45 years of age.
There has now been a total of 34,990 confirmed cases of Covid-19 in Ireland.
Acting chief medical officer Dr Ronan Glynn has pleaded with people to re-double their efforts.
"As we start into this new week, I am asking every household across the country to sit together and make a plan to reduce the number of people you meet this week," he said.
"For people who live in Donegal and Dublin, remember Government advice is to work from home unless it is essential to attend in person.
"For people living in these and all other counties, assume that Covid-19 is circulating in your community, and act accordingly."
Mr Donnelly said that although Cork, Wicklow, Galway, and Louth have cases steadily rising, he does not foresee any announcement on new restrictions being made before Thursday when the National Public Health Emergency Team (NPHET) are due to meet.
Donegal and Dublin have both been ordered into increased local restrictions due to their rising cases, and it is widely expected other counties will follow suit.
"There are four counties which I think will be looked at very carefully. They are Cork, Galway, Louth and my own county of Wicklow," Mr Donnelly told RTÉ's.
"But right now, there are no plans for NPHET to meet earlier, to make any recommendations to Government at this time.
"They meet every Thursday, that may change, but right now they have no plans to meet [before then].
"What happens in each case is the National Public Health Emergency team look at a wide variety of measures.
"They look at not just 14-day rates, but the seven-day rates. They look at where is it coming from, and is it rising quickly? Is it a small number of cases where we've deployed public health to the ground?
Mr Donnelly said he was "cautiously optimistic" about Dublin, but stressed that the seven-day rate must come down before restrictions are eased.
"I have no doubt that people in Dublin have heard this loud and clear," he said. "In the vast majority of cases, people are doing exactly what they need to do just by limiting their interactions."
Meanwhile, the Government's updated travel 'green list' from the Department of Foreign Affairs will come into effect today, with further limits on international tourism.
Germany, Poland, Iceland, and Lithuania have been removed.
Passengers arriving into Ireland from those countries will now be advised to restrict their movements for 14 days, with the Government now advising against non-essential travel to those destinations from Ireland.
The previous 'green list' included seven countries, but has since been reduced to four as the virus continues to spread across the world. The remaining countries left on the list are Cyprus, Finland, Latvia, and Liechtenstein. Liechtenstein does not have an airport.