The announcement to staff came on Budget day and finance workers union IBOA has sought clarification from Ulster Bank that the Central Bank had authorised the move.
The IBOA said that some staff were being relocated from Leopardstown to Georges Quay, but other positions would be outsourced to India.
"IBOA has identified that there must be an agreement in place to accommodate our members' needs before these transfers take place," the union added.
Ulster Bank said that it continues to "leverage the capacity" it has across all of our global operations, to ensure the bank is as efficient as possible.
"We have back-office hubs in the UK, US, Europe, and Asia and, in recent years, have moved a number of roles in and between countries in order to leverage our global capacity to best serve our customers," the bank said in a statement.
"We remain committed to our long-standing principle of situating customer contact work within the country or region where the customer is located."
It is understood IBOA and Ulster Bank management will have talks in the coming days. The Central Bank has been informed of the plans to outsource the jobs.