Some of the top bankers in the United States flocked to a midtown Manhattan law firm on Thursday to make a pitch for managing what could be one of the largest share sales in history -- a secondary offering of potentially $20 billion for bailed-out insurer AIG.

The bankers were expected to offer a cut-rate fee, trading profits for the prestige of managing a historic offering and getting in line for future underwriting business from the company.

Those that are chosen will probably share a fee of around 75 basis points, or about $150 million if the deal hits the $20 billion level, a source familiar with the situation said. That is about half of what they would typically expect for a secondary share offering.

At that size, the AIG offering would rank as one of the 10 largest share sales of any kind in history.

U.S. Treasury Secretary Tim Geithner will meet with AIG Chief Executive Officer Bob Benmosche in Washington on Friday, the Treasury Department said late on Thursday.

JPMorgan Chief Executive Jamie Dimon was among the executives attending the New York meeting. Dimon entered the building of law firm Davis Polk & Wardwell LLP just after 9:30 a.m. EST in New York. Asked how the meeting went as he left, Dimon laughed and said: How'd what go?

Morgan Stanley CEO James Gorman left the building shortly after Dimon's arrival. The bankers on Gorman's team were carrying thick blue folders emblazoned with the U.S. flag. One of Gorman's colleagues carried a bag full of folders.

Gorman also declined to comment.

Bank of America Corp's Brian Moynihan arrived just before 11 a.m. EST.

The appearance of the nation's top bankers was unusual, and pointed to the marquee nature of the offering. In similar situations, banks tend to send sector specialists or other senior executives; sending a CEO lends prestige to the deal and signifies a firm's commitment to winning the mandate.

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Security was tight, with guards keeping a close eye on all the building's entrances and trying to block reporters and passers-by from seeing executives as they came and went.

After a recapitalization deal closes on Friday, the Treasury will own 92.1 percent of AIG. The government rescued AIG from the brink of failure in September 2008 in a bailout that topped $182 billion.

The first share sale is most likely to happen after mid-May, once AIG has filed its financial report for the first quarter with securities regulators, sources have said. The sale could happen as soon as March if conditions were right.

AIG shares closed $1.21 lower at $57.19 on Thursday afternoon on the New York Stock Exchange.

The shares are expected to tumble next week into the mid-$40 range, when recently approved stock warrants begin trading. The warrants, entitling holders to 75 million AIG common shares, were the final key step in the recap deal.

(Reporting by Ben Berkowitz. Editing by Robert MacMillan, Matthew Lewis and Carol Bishopric)