RTÉ News has learnt that Irish Life and Permanent has sent out letters to customers who held accounts with Irish Permanent Isle of Man.
This is to inform them that the Revenue Commissioners will shortly commence an investigation to try to establish the tax status of the accounts.
A spokesman said letters had been sent to all account holders with Irish addresses.
The bank has advised them to consult with a financial advisor over the implications for their tax affairs.
Earlier today, the Chairman of the Revenue Commissioners told the Public Accounts Committee that it is not unrealistic to expect that special investigations will eventually yield over €1bn in unpaid tax.
Frank Daly told the committee that €892m had been recovered as a result of their special investigations to date.
He said that €111m had been recovered from people who held trust accounts with the Bank of Ireland in the Channel Islands.
Inquiries have been carried out into offshore schemes, the non-payment of DIRT and Bogus Non Resident Accounts.
