Figures in the Department of Health are said to believe Ireland's rules for international travel are "far too loose", with Stephen Donnelly reportedly fearful of a major Covid-19 spike as more people come into the country over Christmas.
The Department of Health is understood to be concerned that a lack of mandatory quarantining – added to the likelihood of many Irish people abroad coming home for Christmas – could lead to a big increase in case numbers, the Sunday Independent reports.
The Minister for Health has already expressed his concerns about Ireland's lack of border controls, amid reports of a "pushback" from the Department of Health ahead of the introduction of new travel rules last Monday.
Mr Donnelly had a call last week with the chief medical officer in Victoria, Australia, where international travellers have to quarantine when they enter the state.
And he aired his views on Ireland's travel rules before Ireland's sign-up to the EU's "traffic light" system for international travel.

The current regulations for travelling into Ireland mean even those coming from red-zone EU countries will be able stop restricting their movements after November 29, if they receive a negative PCR test a minimum of five days after arriving in the country.
A Government spokesperson confirmed to the Irish Mirror that the same rules are in place for those travelling into Ireland from countries outside the EU.
Senior figures in the Department of Health are also reportedly concerned that Ireland's system for recording coronavirus cases is giving a "misleading comfort to some people".
Only those directly infected by a person who travels from abroad are categorised as travel-related cases – meaning secondary infections aren't classified as related to travel.
This means the number of cases in Ireland is actually "far, far greater" than many people think, the Sunday Independent reports.
Last week, the Tanaiste delivered a stark message to families across Ireland when he warned Irish people abroad not to book flights home yet.
Leo Varadkar admitted his message was a "tough" one for people to hear, but added: "Christmas is six weeks away and it’s too soon for people to be booking flights to come home."