The State has changed the price range at which it will sell shares in AIB in its flotation later this week.
The development shows there is strengthening demand for the stock.
The shares had originally been priced between €3.90 and €4.90 but this has been revised to between €4.20 and €4.60.
The Government's advisers on the flotation told the stock market today that the shares have been "oversubscribed multiple times".
They said investors are prepared to buy shares in the "upper half" of the revised range.
The flotation will proceed at 8am on Friday morning.
The State will sell 25% of the bank but it has the option to sell more share if there is sufficient demand.