Many offshore account holders may escape the Revenue because the tax authorities have no power over customers of foreign-owned banks.
According to a report in the Irish Times, at least four of the 10 Irish financial institutions that agreed to co-operate in the recent trawl of offshore accounts are subsidiaries of foreign banking groups.
As a result, they will not come under new Revenue powers granted in the Finance Act 2004, which facilitates the clampdown on offshore accounts.
The Revenue Commissioners announced in the middle of February a campaign to pursue the holders of offshore accounts, including those held in Northern Ireland.
As part of the campaign, Mr Daly met executives of Irish banks, which had associated or subsidiary businesses offshore. These include AIB, Bank of Ireland, Ulster Bank, National Irish Bank, Permanent TSB, Anglo Irish Bank, First Active, ACC Bank and EBS Building Society.
Between them their foreign subsidiary and associated operations sent 120,000 letters to all customers who had addresses in the Republic.
However, it is now uncertain how the Revenue will track down customers at four of these banks - Ulster, National Irish, First Active and ACC, which are owned by groups in Britain, Australia and the Netherlands.
They, along with other foreign-owned banks such as IIB and US banks with operations here, do not fall under the new provisions in the Finance Act 2004.
According to the report, this could thwart efforts to collect up to €1bn in outstanding penalties and tax.