Mr Varadkar said the Department of Health and Government have insisted mandatory quarantine would not be practical.
"Australia tried mandatory quarantine and it turned out to be a bit of a disaster.
"The centres, the hotels in which they quarantine people became clusters for infection and now Melbourne is in a second lockdown."
Mr Varadkar said the Government intends to publish a "green list" of countries where it safe to travel to and from without having to quarantine next week.
The Blue Haven Hotel in Kinsale is one of a number of businesses asking international travellers to stay away for 14 days.
Hotel management said that although staff are looking forward to being able to welcome everyone that walks in their door very soon, that “for now to keep everyone safe, we request that all guidelines are adhered to prior to us being able to do so”.
“In the interest of public safety and in complying with the government policy, we kindly ask that individuals and groups visiting from outside of Ireland, who have not completed 14 days of self-quarantining, please do not enter the premises until you do," they said.
Currently, it is not legally mandatory for someone to be detained to ensure they are self-isolating but anyone arriving into the country must fill out a passenger locator form.
The Echo took to the streets of Cork yesterday to ask people their opinion about letting international visitors into the country.
Here is what they had to say:
Eoin Nash - Ballincollig
Bridette O'Connor - Farnanes
Mary McCarthy - Carrigaline
Ann Burke - Cork city
Michelle O'Brien - Fair Hill