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Alibaba’s IPO was long expected to be a blockbuster but even so the huge flood of orders is stunningly greater than the anticipated number.

On Friday, people briefed on the matter said that Alibaba’s underwriters have told their sales staffs that they plan to close orders for the stock sale by Wednesday, this in just 5 days into the journey to promote itself to prospective buyers.

And with the intense interest in Alibaba’s IPO — shown by the flocks of investors who waited to spend even an hour with Alibaba’s senior management — signals at the possibility of company’s bankers eventually raising the price range for the Alibaba’s IPO, meaning that they might push it past the initial goal of raising funds of $21.1 billion. That would make Alibaba’s IPO the biggest IPO in the history, leaving the Agricultural Bank of China in second place which raised $22.1 billion four years ago . But the people briefed on the matter, who spoke on the condition of anonymity, cautioned that no plans had been set and that the price range for Alibaba’s IPO might remain within the already disclosed $60 to $66 a share, which values the company at roughly $163 billion at the high end.

Alibaba’s IPO will be priced after the underwriters examine the orderbook and a final decision will be made next Thursday.

The sales staff was informed on Friday by the underwriters that the stock offering was already oversubscribed and that the found no sensitivity to the existing price range. This may mean that the banks might be comfortable raising the price of Alibaba’s IPO, similar to the cases of General Motors and Facebook but the banks should be wary of pushing the price range too far lest they should scare off the investors.

Since Alibaba began its roadshow on Monday, money managers ranging from huge mutual funds to big-name hedge funds have clamoured for an audience with executives including the company’s chairman and co-founder, Jack Ma. More than 800 people attended an invitation-only lunchtime presentation at the Waldorf-Astoria in Midtown Manhattan, with some others turned away for lack of space.

Other presentations across the country this week were smaller but no less packed. A gathering with Fidelity Investments portfolio managers and executives in Boston on Tuesday, for example, drew more than 100 attendees, according to people at the event.

Many hedge fund magnates, including Daniel S. Loeb of Third Point, have sought out one-on-one meetings with the Chinese company’s management, according to people with direct knowledge of the roadshow scheduling. But Alibaba’s underwriters have allotted fewer than 40 of the roughly 100 planned meetings to individual firms.

Most of those meetings will go to the institutional investors considered crucial to the offering’s success, including mutual fund giants like BlackRock and Fidelity and sovereign wealth funds in the Middle East and Asia.

Still, prominent hedge fund managers have gotten an intimate audience with the company. Mr. Loeb and several other investors — including David A. Tepper of Appaloosa Management, Louis M. Bacon of Moore Capital Management and Chris Shumway of Shumway Capital — attended a private lunch with Alibaba executives on Wednesday, according to people with direct knowledge of the schedule.

Several of those investors, Mr. Loeb and Mr. Tepper among them, walked away with good impressions of the management team, some of these people said.

Representatives of Alibaba and the hedge funds declined to comment or were not available for comment.

If any of these investors have not placed orders for shares in the company, they will have only a few more days to do so. In their communications to the sales staffs, the underwriters said that they would stop accepting orders from investors in the United States by Tuesday at 4 p.m. Asian investors have until 4 p.m. Hong Kong time on Wednesday to place their orders, while money managers in Europe have until the close of business in London on Wednesday to submit orders.

But investors who have not met with the company’s executives — either in one-on-one gatherings or in small group sessions — by their region’s deadlines will have extra time to file their purchase orders.