Some of the United States' top bankers descended on a law firm in midtown Manhattan on Thursday to pitch for what could be one of the largest share sales in history -- a secondary offering for bailed-out insurer American International Group Inc.

JPMorgan Chief Executive Jamie Dimon was among the executives attending the meeting. Dimon entered the building of law firm Davis Polk & Wardwell LLP just after 1430 GMT in New York. He declined to comment.

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

Gorman also declined comment.

Bankers are expected to come and go throughout the day to make their case for managing a share sale that could exceed $20 billion.

Sources told Reuters on Wednesday that bankers were expected to pitch a fee structure of 75 basis points or less -- low for a secondary offering, but still worth perhaps $150 million in fees to the winning banks if the share sale reaches $20 billion.

After a recapitalization deal closes on Friday, the U.S. 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.

AIG shares were trading 11 cents higher at $58.51 on Thursday morning on the New York Stock Exchange.

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