It comes as the National Public Health Emergency Team (Nphet) met yesterday to consider the spread of the virus around the country, after Government rejected its recommendation to move to Level 5 restrictions this week.
No new restrictions have been recommended following the meeting, though the team has said it remains “deeply concerned”.
Fines for for people who leave their county for non-essential reasons were confirmed as under consideration by Government on Wednesday by Taoiseach Micheál Martin.
It came amid reports that Tánaiste Leo Varadkar had proposed a system of graduated fines - which could include €50 penalties for not wearing a face mask and €200 penalties for leaving a person’s county - to his parliamentary party on Tuesday night.
Sources present at the Fine Gael parliamentary party meeting told the Irish Times that Mr Varadkar said the previous system of €2,500 fines for those who break Covid-19 regulations was seen as draconian, and that a system of graduated fines should be considered instead.
On Wednesday, a Government spokesperson said the Government had no immediate plan for a new system of fines for breaching public health guidelines though "all options are under review."
Fines of €2,500 are already in place for breaches of public health regulations such as organising a public gathering or not wearing a mask on public transport.
Gardaí have recommenced Operation Fanacht to support compliance with new Level 3 restrictions around the country to curb the spread of Covid-19.
Some of the restrictions in the Government’s Living with Covid-19 plan carry fines or prison sentences while others rely on the public's willingness to adhere to the measures.