The Transport Minister says the government will be stepping up the systems for managing tourists coming into the country.
But Eamon Ryan says they won't be stopping all flights from the US or other countries.
Cabinet Ministers are meeting this afternoon and part of the discussion will be a stepped up method of tracking whether people coming into the country are self-isolating.
However, Eamon Ryan says the number of tourists is very small.
The Green Party leader says: "We will be stepping it up. A lot better system of monitoring people and following up.
"The number of flights, there is a lot of concern about the States (US) and it is something we really have to look at it.
"Typically, there is about three flights, maybe four flights a day, very small numbers about 250 people yesterday in total.
"And looking forward to the next three weeks it is the same story."
The Transport minister's comments follow the Taoiseach's statement this weekend that it is "too early" for British tourists to come to Ireland without quarantining for two weeks.
Micheál Martin said that due to a rising reproduction rate, and noting the UK's "difficulties" with suppressing the virus.
Meanwhile, a Trinity Professor has said that it is "disgraceful" to allow American tourists into Ireland.
Professor Luke O'Neil said that allowing tourists into Ireland from the US is a "surefire way" of increasing cases of Covid-19.