A spokesperson for Ulster Bank also declined to comment on the report
The Financial Services Union (FSU) has described the Irish Times report as “extremely worrying”.
“The FSU has contacted Ulster Bank and the Minister for Finance to demand clarification and answers,” said John O’Connell, FSU General Secretary.
“This is a very stressful time for staff and customers. It is simply not good enough for staff to find out through the media that NatWest is winding down Ulster Bank operations in the Republic of Ireland.”
Mr O’Connell added that if Ulster Bank is to exit the Irish market, any solution must involve the maximum protection for customers, staff jobs and the branch structure.
A spokesperson for Ulster Bank also declined to comment on the report.
NatWest has been conducting a strategic review of Ulster Bank’s Republic of Ireland operations since September.
It is due to report its annual results for 2020 on Friday morning and the expectation is that it will provide an update at that time on the review amid growing speculation about its intentions.
Ulster Bank has 1.1 million customers here, along with 2,800 staff and operates 88 branches.
It has operated in the Republic of Ireland for 160 years and has €20.5bn in loans in the Irish market, so any decision to exit would have significant implications.
The bank has been reviewing its operations because it has struggled to perform in recent years.
The Minister for Finance said recently that the consequences of Ulster Bank withdrawing from the market here would be “very serious” for the economy, employment and credit.