The State's shareholding in AIB is held in the ISIF's (Ireland Strategic Investment Fund) directed portfolio. In order to take any action in relation to the State's shareholding in AIB I would write to the ISIF and direct it accordingly.
To complete the repair of the banking system and ensure that banks are supporting the wider public interest, the Program for a Partnership Government allows for the sale of not more than 25% of any bank before the end of 2018 (plus any over-allotment option). Consistent with precedent, the decision to proceed with a IPO of AIB would likely be a decision for government.