Plans by SIPTU to demolish Liberty Hall and replace it with a 22-storey building on the historic site have been appealed to An Bord Pleanála.
The board will decide in the coming weeks if it will hold a oral hearing on the proposal or whether the case will be decided in private.
It confirmed it had received two appeals, including one from Irish Life.
It is understood Irish Life raised issues about the proximity of the proposed tower to their building at Beresford court. It also raised concerns about the increased width of the new building.
In its appeal, Irish Life says the proposals would represent "an overdevelopment of the site in the context of the surrounding urban fabric".
The deadline for appeals is this evening.
Last month, Dublin City Council granted the union planning permission for the new building, which would be 35% higher than Liberty Hall.
The permission is subject to 19 conditions, including a further alignment of the north side of the building, particularly at the upper levels.
Proposals for the site also include a four-storey heritage centre at the top of the building, with a public skydeck accessible by a glass-fronted lift.
A conference centre and theatre have also been proposed, along with 17 storeys of offices.
It was SITPTU's second proposal for the site.
The union has said it will begin the process of preparing its response to the appeals.