BNY Mellon has been chosen by the Government to manage the the Apple escrow account, according to a report in the Irish Times.
The US bank will act as custodian to oversee the management of more than €13 billion of taxes and interest the country has been ordered to collect from Apple.
The Department of Finance and the National Treasury Management Agency, which is in charge of the procurement, declined to comment.
However, Minister for Finance Paschal Donohue said they were entering the last few days of a cooling off period for the procurement process and when that is complete he will issue a statement to confirm who will be managing the account.
The Bank of New York Mellon Corporation is a US worldwide banking and financial services holding company headquartered in New York City.
It also has operations in Ireland, where it employs 1,800 people in Cork, Wexford and Dublin.
It is believed that the process of establishing an escrow account has so far cost the State €2.5m.
Apple was ordered to pay the back taxes after the European Commission ruled that the tech giant had received unfair tax incentives from Ireland.
Both Apple and Ireland are challenging the ruling at the European Court of Justice.