Options are being prepared for the Irish government on how to restrict non-essential travel from countries outside the UK and European Union, according to the Republic's health minister.
Stephen Donnelly said he was "concerned about high rates" of coronavirus in some countries, in a tweet on Sunday.
The number of travel-related cases in Ireland is currently thought to be low.
However, Mr Donnelly said "the risk is increasing".
Many are asking about travel/tourists coming into Ireland from countries with high Covid rates. My Dept is preparing options for Gov on how to restrict non-essential travel from third countries (outside EU/UK) with high rates of Covid. Am concerned about high rates in some places— Stephen Donnelly (@DonnellyStephen) August 9, 2020
According to the minister, his department will finish the proposals "as soon as possible" and present them to government for discussion.
On Friday, restrictions were put in place in Kildare, Laois and Offaly restricting residents from traveling beyond those counties, except in limited circumstances.
Speaking after they came into force, Mr Donnelly said the government was "investigating measures" surrounding non-essential international travel.
He added that the government had put in place a range of additional supports for the affected counties, including "additional testing and public health capacity, and isolation accommodation for those who need it".
"Outbreak control teams are in place for all outbreaks. The HSE has also established a National Standing Committee to consider and address matters related to the food processing and construction industries more generally given the recent pattern of cases," he added.
A 'green list' for international travel was published by the Irish government in July, outlining countries you can travel to without having to enter a 14-day quarantine on return.
Cyprus, Gibraltar, Malta, Monaco and San Marino were removed from the list last Tuesday, when the government also decided not to move into Phase Four of its Covid recovery plan.
Advice from the Republic's National Public Health Emergency Team remains that all non-essential foreign travel should be avoided, regardless of whether or not a country is on the green list.
On Sunday, the Irish Department of Health said there had been no further coronavirus-linked deaths and 68 additional confirmed cases.
It said the death toll in the Republic of Ireland remains at 1,772.
Acting Chief Medical Officer Dr Ronan Glynn, said: "We continue to see cases linked to the outbreaks in counties where additional public health measures have been introduced.
"This was expected and we will continue to monitor closely.
"From tomorrow face coverings will be mandatory in retail and other indoor settings like hairdressers, cinemas and museums.
"We know that most people are already wearing face coverings and we hope to see even greater uptake over the coming days."