AIB's IPO is expected to happen in the coming weeks ahead of the selection of Fine Gael's new leader on June 2, which will mark the end of Michael Noonan's spell as Minister for Finance.
The Dáil passed a private motion to delay the privatisation yesterday as many TDs from the Government failed to vote.
The Labour proposal called for the sale to be stalled until the EU's fiscal rules have been renegotiated.
AIB's sale can go ahead as planned despite yesterday's vote.
Both The Irish Times and Irish Independent report this morning that sources have told them that the sale is imminent.