RTÉ News understands that Canadian Imperial Bank of Commerce is the bank which has made a high-level approach to the Government and AIB about the possibility of taking a minority stake in AIB Group.
Earlier, AIB confirmed that it had received an approach but did not comment on the identity of the bank involved.
AIB said any talks were preliminary and were not expected to progress until there was greater clarity on other issues such as the National Asset Management Agency.
In a brief statement, a spokesman for CIBC said it did not comment on market rumours or speculation.
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CIBC is one of Canada's biggest banks, with around 40,000 employees worldwide. It has more than 1,000 branches across Canada.
AIB has a 24% stake in a US based-bank M&T, which could potentially be of interest to a North American bank. It is understood that executives of the bank had discussions at a senior level with the Department of Finance.
In its latest results - for its second financial quarter to the end of April - CIBC reported a small loss of C$51m (€33m), but its shares fell as it also reported a big jump in provisions for credit losses. It is due to report third-quarter results on August 26.
The Canadian banking system has been more resilient than those in many other big economies, and its banks have not had to be supported by the country's government.
The big strength of Canadian banks is their retail operations - they have huge deposit bases. Canada's banks also took a more conservative approach to lending.
While there are certain pockets of expensive areas for property in Canada, there was never any massive property lending boom.
