The Irish Times reports that the unnamed financial institution will complete the deal once AIB has been cleared of its risky development loans, which are to be moved to the government's National Asset Management Agency (Nama).
An unnamed source told the publication that the deal is being seen as a long-term acquisition that may not take place in the immediate future.
"I don't think they're going to be moving quickly until they see the full extent of Nama," the source was quoted as saying, adding: "We deem this to be of a lot higher standard than other approaches."
The Canadian bank is believed to be one of the country's biggest five financial institutions, which are, according to Reuters, Royal Bank of Canada, Bank of Montreal, Bank of Nova Scotia, Canadian Imperial Bank of Commerce and Toronto-Dominion Bank.
Earlier this month, AIB announced a half-year operating profit of $2.45 billion, a decrease of six per cent.