Scammers are taking names from publicly available shareholder lists
Older people are being asked to be particularly vigilant against a new money scam.
The Irish Independent reports there has been a spate of attempts by swindlers from overseas companies cold-calling investors, trying to scam money from them.
The operation seems to target people over the age of 55 who own shares and it uses pressure tactics - like forcing owners to act quickly or make decisions for a so-called special deal.
The offer to purchase shares will likely come with a request for bank details or money up front as a bond or other form of security.
This will be accompanied by a guarantee to pay back the money involved if the sale does not go ahead.
This advance fee is part of the scam - investors are unlikely to hear from them again.
The Irish Stock Exchange (ISE) say they were made aware of a potential investment scam back in February.
These so-called "boiler room scams" are operated by fraudsters who contact investors unexpectedly, and offer to buy their shares at prices higher than current market value.
These unauthorised individuals and companies get investor information and contact details by accessing publicly available shareholder lists.
The ISE says: "Investors are reminded to be vigilant - if it sounds too good to be true, it probably is".
It is reminding investors that if they are in receipt of unsolicited contact from someone offering to buy their shares, that they should:
If a firm is not on the Central Bank register, they should not be offering financial services.