Michael Noonan could give the green light to the flotation of AIB during his final days as Minister for Finance this week.
The sale of existing shares in the bank, is set to be the biggest flotation on the Dublin and London stock markets this year.
The sale which equates to about a quarter of the AIB shares should raise between €2.5bn and €3bn.
But the Labour Party Leader Brendan Howlin wants Independent Ministers to block the move.
"I think there is no legitimacy at all in a decision being made by a Cabinet that in its current makeup will not be there much longer.
"They should leave it to the incoming Cabinet to make a decision, and if the decision is the same the incoming Cabinet should seek the approval of Dáil Éireann - that's what democracy is," he said.