The Government is planning to increase the €500 fine for going on holidays abroad to €2,000.
It would mean a couple traveling abroad on for a non-essential journey could face a €4,000 add-on bill if stopped on the way to the airport.
The €500 fine came into effect in recent weeks, as part of a range of measures introduced to limit non-essential travel abroad.
Speaking in the Dáil, Taoiseach Micheál Martin said he has asked the Health Minister to increase the fines.
He said: "About 60% of those travelling are returned Irish holidaymakers.
"There's a sense the €500 is not sufficient disincentive to travel abroad - the Government is considering increasing that to €2,000, to act as a significant deterrent."
It comes as new figures reveal that 5,241 people arriving at Dublin Airport last week were Irish residents returning from holiday.
In total, 13,556 people arrived into Dublin Airport from overseas last week for various reasons - 8,218 Irish residents and 5,388 non-residents.
It means 63.8% of the Irish residents arriving into Dublin Airport last week were returning from a holiday.
Liz Canavan from the Department of Taoiseach says people shouldn’t be going on holiday during a pandemic.
She said: "While overall passenger numbers are a tiny fraction of normal levels - below 3% for this time of year - over half of the passengers arriving into the country are Irish residents, and two-thirds of those are returning from holidays.
"This is a very concerning statistic - while we would all love and need a holiday, now is not the time to travel."