The initial public offering for AIA could raise up to $20 billion this month, making it the world's second biggest IPO this year.
And the firm looked well on course to achieve that as investors snapped up shares, which went on sale Monday, the Wall Street Journal said, citing people familiar with the situation.
It said the sale may have to close on Tuesday rather than Thursday.
AIG plans to price the deal on Friday.
AIA's management has been holding roadshows for the past two weeks as it sought investment from large institutions to buy as much as two-thirds of the company from AIG, it said.
Announcing details of the sale at a press conference in Hong Kong Sunday, AIA said it will initially offer 5.86 billion shares at between $18.38-$19.68 Hong Kong each. It is looking to raise up to 15 billion US dollars.
However, it said it could issue up to 8.08 billion shares if it exercised a greenshoe option, which would bring the total raised to around $20 billion and leave AIG with a stake of just 32.9 percent stake.
AIG, which is looking to repay US taxpayers after a government bailout in 2008, won approval last month for the sale.
AIG was forced to look at publicly floating AIA in Hong Kong after the collapse in June of a 35.5-billion US dollar takeover bid by Prudential.
Among confirmed cornerstone investors are the Kuwait Investment Authority, the oil-rich Gulf emirate's sovereign wealth fund, and a number of Hong Kong tycoons.
Chinese sovereign-wealth fund China Investment Corp is also among the buyers, the report cited one of the people close to the situation as saying.
Earlier this year, Agricultural Bank of China raised a total of $22.1 billion from an IPO, exceeding the previous record set by the Industrial and Commercial Bank of China, which raised $21.9 billion in 2006.
Trading in AIA is expected to begin on October 29.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional