The Revenue has given them until March 29 to make a full settlement for their liability or face a full investigation. Based on figures from previous inquiries, the probe could net hundreds of millions for the Exchequer.
Tens of thousands of letters have been sent by the main Irish banks to customers who held offshore trusts in the 1980s and early 1990s, advising them to make a settlement with the Revenue.
Customers who come forward before March 29 will not be prosecuted and their names and details of their tax settlements will not be published in the tax defaulters list.
After that, the Revenue's Offshore Assets Group (OAG) will use new powers to compel banks to open up their books and track down the remaining tax evaders. If caught by the OAG they face larger penalties and possible prison sentences.
The move was prompted by a meeting between chief executives of 10 Irish banks and the chairman of the Revenue Commissioners, Frank Daly, last December.
Although there is no firm number of how many offshore trusts were set up by the banks, Revenue sources say the number is likely to run into the thousands.
Last year the Revenue investigated customers of the Bank of Ireland Jersey Trust company. A trawl of its customers saw 254 people come forward and make a voluntary settlement, which netted Revenue €105 million in interest, tax and penalties, an average of €400,000 each, although one individual did make a €7m settlement.
A separate investigation of customers of Irish Permanent's Isle of Man branch began last November.
Offshore trusts are not illegal, but individuals must declare income earned from the trust to the Irish tax authorities. The accounts were normally set up by wealthy individuals but the scale of the new probe suggests they were much more common.
While thousands of people are likely to be hit with severe penalties, it is doubtful whether any financial institution which knowingly aided a tax evader will ever be prosecuted.
To date, the Revenue has collected €606 million in settlements from individuals who held bogus non-resident accounts, while close to €300 million has been taken from other Revenue investigations into tax evasion schemes.