The Government has asked Bank of Ireland to alter its plans to raise funds so that the State's shareholding in the lender will not be diluted.
Under a range of scenarios published by the bank on Saturday, the State's minimum shareholding in the bank, after it issues new shares, would be 32%.
If no private investors are willing to take new shares in the bank, the State's stake would be a maximum of 87.7%.
The company is currently finalising plans to raise €5.2 billion to meet requirements of stress tests conducted by the Central Bank.
As part of Bank of Ireland's fund-raising, it will try to sell new shares and offer junior bondholders the opportunity to swap bonds for shares.
Under an earlier plan, the Government's shareholding could have been reduced if private investors bought shares in large numbers. That has now been altered so that the State can maintain its existing shareholding.