An Post is considering moving its headquarters out of the GPO to cut costs.
It's also looking for 300 staff to volunteer to take redundancy.
In a statement, the company said the latest offering is for managers and staff across its corporate centre and support services.
It has identified in excess of 250 full-time roles that could be made redundant.
If administration staff are moved out of the building, it's understood a post office would remain, as would An Post's Witness History tourist attraction.