An Post is seeking up to 300 voluntary redundancies over the coming months.
It is part of the companies cost-cutting measures - which may also see the move of it's headquarters from Dublin's O'Connell Street to another location.
The company says, the retail Post Office, parcel hall and 'Witness History' Visitor Centre will remain in place at the HQ.
Head of Corporate Communications with An Post, Anna McHugh says the building needs urgent work.
She said: "We are looking at options because we really do need to do a serious job on the building - It's about 35 years since it was done.
"Obviously we are doing running repairs all the time and really great maintenance, but it's a listed building so every window, door and tile has to be checked in keeping with a listed building."