The Cabinet is due to meet today to discuss matters including last week's cyberattack on the HSE's IT systems.
Ministers will be briefed on the attack and its impact on the health service, with the HSE saying the disruption caused could last "well into this week".
The Irish Times reports there are fears within the Government that patient data may be "abused" by the people responsible for the attack, however, no ransom will be paid in line with State policy.
Cybersecurity experts are now monitoring the dark web for data harvested during the attack on the HSE as it is thought the group responsible may either sell the data, or publish it online if they do not receive the ransom payment.
On Monday, Taoiseach Micheál Martin, Tánaiste Leo Varadkar, Minister for Transport Eamon Ryan, Minister for Health Stephen Donnelly, Minister for Justice Heather Humphreys and HSE chief executive Paul Reid were briefed by the National Cyber Security Centre (NCSC) on the matter ahead of the full meeting of Cabinet today.
Work is ongoing to put the HSE's IT systems back online after they were shut down on Friday as a precautionary measure, however, no disruptions are expected for payroll services.
Other matters due for discussion at today's Cabinet meeting include a proposal to block investment funds from buying large stocks of residential properties, while changes to restrictions surrounding international travel will also be debated.