The Unite trade union has written to the Minister for Finance and the Minister for Public Expenditure requesting a meeting regarding banking jobs.
The union has said it is very concerned that a significant number of jobs in the banking sector could be wiped out as part of plans to restructure the country's financial sector.
Unite will also meet with the Central Bank on Monday.
The union represents 5,000 members in four different banks.
It is particularly concerned about the future of Permanent TSB which, it says, did not feature strongly in yesterday's discussions.
The union is to write to its members today with a response.