National Irish Bank (NIB) and Northern Bank have written to their staff members to confirm that a final decision on the future of the two banks will not be made until January. Both banks are owned by National Australia Bank (NAB).
The move follows a Friday meeting at which the Irish Bank Officials' Association (IBOA) sought pledges from the two banks on its members' jobs.
The IBOA - which represents about 1,500 staff in Northern Bank and 700 staff in NIB - said yesterday that it had been assured that neither branch closures nor staff cuts were on the agenda.
The union said it hoped the assurances would bring some "temporary respite for worried staff and customers".
IBOA general secretary, Mr Larry Broderick, said the association would also make representations on behalf of its members to potential bidders for the two banks.
It is believed that two international banks are continuing to discuss a possible purchase of NIB and Northern with their Australian owner.
A weekend news report suggested that Dutch bank Rabobank had emerged as the most likely buyer.
It had previously been thought that Rabobank had pulled out of the process before making a formal bid because it had limited interest in entering the Northern Ireland market.
A spokesman for Rabobank declined to comment on "market rumour".
Most bidding speculation to date has centred on Scottish bank HBOS which is believed to have been unwilling to meet NAB's expectations with a bid for the banks.
It is unclear at this stage whether the bank has exited the process entirely. Market sources also suggested last night that the identity of all interested parties may not yet have emerged.
NIB and Northern have been valued at between €1.2 billion and €1.5 billion. The IBOA will meet NAB again next month.
"IBOA believes it is vitally important that the issue of the banks' future ownership is sorted once and for all and as soon as possible," said Mr Broderick yesterday.