Gardaí have said the reports they receive will be handled in a "sensitive manner".
Gardaí are urging people who believe they are victims of cyber-related crime to contact their local Garda stations, following the recent cyber attack against the HSE.
Last Friday, the HSE announced it had temporarily shut down its IT system after it was targeted in a "significant ransomware attack", causing major disruptions to health services across the country.
The group behind the attack still has access to all the data that was taken during the hack and is expected to release the data online unless a ransom is paid.
Both Taoiseach Micheál Martin and HSE CEO Paul Reid have said a ransom will not be paid to the perpetrators of the attack.
Earlier today, Minister for Health Stephen Donnelly said it is
"entirely possible" there will be a "data dump" of HSE data on Monday.
In a statement, a Garda spokesperson said the Garda National Cyber Crime Bureau (GNCCB) is continuing its criminal investigation into the cyber attack together with local and international partners.
Addressing claims some data may have already leaked online, the Gardaí statement said: "It has not been confirmed with full certainty that personal records or data reported to have been circulated are in fact genuine even though this is probable and would be a feature of these attacks.
"In general, our crime prevention advice has been and remains - if you are contacted by persons stating that they have your personal details and/or are looking for bank account details, you should not engage or provide any personal information."
Gardaí are encouraging people to report any suspected breaches of personal data, which will be examined by specialist investigators.
They say such reports will be handled in a sensitive manner.
