A deal would be among the biggest ever on the Irish Stock Exchange, which is seen as the most likely venue for a primary float.

While tax payers would reap the vast bulk of the cash, an IPO will prove a bonanza for brokers, underwriters and corporate law firms, who will expect to pick up around 1pc of the value of any deal in fees for nursing the bank back onto the markets.

Panels of brokers and banks that will advise the Department of Finance on bank privatisations are due to be named in the next 10 days.

The financial advisers are being appointed to three panels, and specific underwriters and advisors to work on sales of the State’s stakes in AIB, Bank of Ireland and eventually Permanent TSB will be selected from the panels.

Selling AIB, which cost €20.8bn to bail out, is by far the most important element in the bank privatisation plans. A spokesman for the Department of Finance confirmed yesterday that it has written to investment banks and corporate advisors in recent days advising them that they will be named to the official panels of approved financial advisors to the Government in the next 10 days.

It’s thought a mix of international and Irish firms have made the cut.

The first panel covers socalled capital markets – where bonds and shares are listed and traded, and strategic and restructuring advice with a heavy emphasis on the State’s privatisation strategy. The second panel will deal with general financial advice, while the third is to select potential “bookrunners”, a term for banks that manage bond and share sales.

Six out of seven of a separate panel of legal advisors that have been previously named are Irish.

Valuations of AIB are increasing rapidly after the bank returned to profit this year.

Profits AIB’s annual results due to be published on March 31 will be the starting trigger for a sale of between 25pc and 30pc of the bank through a partial stock market flotation, according to Ciaran Callaghan of Merrion Stockbrokers, who was previously an analyst at the National Treasury Management Agency (NTMA).

Those results are expected to confirm AIB’s first full year of profits since the crash.

The bank is now likely to command a price on the market of around 20pc more than its so-called book value, which was €11.229bn at the end of July, according to Mr Callaghan.

That is based on a peer comparison with Bank of Ireland, which trades on the market at a price equal to 1.4 times its net asset value.

At €3.4bn, even a partial flotation of AIB would be among the biggest ever on the Irish Stock Exchange, but would still leave the bank in majority state hands.

A share sale would have significant implications for other AIB shareholders, who between them own just under 1pc of the bank.

The 11.5 cent each of those shares are currently trading at is wildly overvalued by any rational measure, suggesting a valuation closer to 6 times book value than the 1.4 times at Bank of Ireland.

Once 25pc to 30pc of the bank is back on the market, the more liquid newly priced new shares would quickly swamp the old over-valued stock, bringing prices down.

Politically, timing a deal to recoup cash from AIB ahead of a general election expected in late 2015 or early 2016 could prove a boon to the Government. But there is no hope of getting back the full amount ploughed into the bank in the next 12 to 18 months.

AIB declined to comment.

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