Demand is so high for orders in Alibaba's IPO that the company may close the book early. Getty

In the centuries-old fairy tale, poor woodcutter Ali Baba stumbles across a horde of treasure hidden in a cave, survives plenty of misadventure and chaos, and ends up the only one alive who knows the secret of the treasure and the magic words that open the cave. Investors who are able to snatch up shares of the modern-day Alibaba, the Chinese e-commerce giant preparing for its initial public offering next week, may feel almost as lucky.

Demand for the company’s hotly anticipated IPO is so big and oversubscribed that Alibaba’s banks expect to close their order books as soon as Tuesday, according to several reports. The firm’s underwriters told their salesmen on Friday morning to close all orders from U.S. investors by Tuesday afternoon, sources told the New York Times, adding that they might push the IPO’s fundraising goal beyond $21.1 billion and the offering price above the current expected range of $60 to $66 a share. International investors will have until Wednesday to place their orders.

When Alibaba launched its road show to make investor presentations on Monday in New York City, a crowd of 800 investors from hedge funds and mutual funds snaked through the hallways of the Waldorf- Astoria Hotel. Other presentations in Boston and Baltimore have been mobbed, and crowds lined up early to gain access to today's stop in San Francisco.

Typical for such large IPOs, such as those for Facebook Inc. (NASDAQ:FB) and Twitter Inc. (NYSE:TWTR) in recent years, the offering is largely unavailable to the average investor. About 40 large institutions have requested orders over $1 billion, reports CNBC, while orders from “friends and family” (employees and people close to Alibaba) total over $1.5 billion.

"It's totally pathetic," Michael Cohn, chief market strategist at Atlantis Asset Management, told NBC News. "The public's just not allowed to participate. The large fund people that manage money for, just say, the Fidelitys, the Vanguards of the world and the hedge funds, are the ones that get the largest allocation."

When it debuts on the New York Stock Exchange on the expected date of Sept. 19 with ticker symbol BABA, it could be the biggest tech IPO in history.