Facebook will close the books on its $10.6 billion initial public offering and stop taking orders Tuesday, two days ahead of schedule and a signal that the Silicon Valley IPO is drumming up strong demand, according to a source familiar with the deal.

Furthermore, Facebook is planning to increase the price to a range of $34 to $38 a share, a person with knowledge of the matter told The New York Times' DealBook Monday evening.

At the top of the range, the world's largest social network's would be valued as high as $104 billion, when it starts trading later this week. On May 3, Facebook set the estimated price for its IPO at $28 to $35 a share. At the midpoint of that range, Facebook would have a market value of $86 billion 

The No. 1 social network is scheduled to price its shares Thursday, then begin trading on Friday. The IPO is already well oversubscribed, which is why the social network is closing its books earlier than anticipated, Reuters and Bloomberg both reported, perhaps citing the same source, who asked not to be identified because discussions with the company are private.  

They're swamped with the orders that are in, Jon Merriman, chief executive officer at investment firm Merriman Holdings Inc. (MERR) in San Francisco, told Bloomberg. They just need time to determine the price. They can send the message -- the books are closing, send in your orders now.

No decision has been made about raising the proposed offer price for Facebook shares, which are being offered at $28 to $35 each. If the price range is increased, it will likely be done after final orders come in Tuesday. Given the size of the IPO, the deal's underwriters are likely to be very cautious about raising the price range, the source said.

If Facebook's underwriters choose to raise the deal's price range more than 20 percent, the company will need to file an amendment with the Securities and Exchange Commission.

Company spokesman Jonny Thaw declined to comment on Monday.

The world's top social-networking site is seeking a market value of as much as $96 billion. At that level, Facebook would surpass United Parcel Service Inc. (UPS) as the most valuable company in history to go public in the U.S., based on market capitalization, data compiled by Bloomberg and Dealogic show. 

Facebook will continue with its roadshow for the rest of the week, said a second source familiar with the deal, and investors who haven't yet attended a roadshow presentation will still be able to place orders.

Company executives met with prospective investors in Chicago on Monday and are slated to travel to Kansas City and Denver, before returning home to Menlo Park, Calif.

The IPO comes amid concerns from some investors that Facebook hasn't yet figured out a way to make money from an increasing number of users who access the social network on mobile devices such as smartphones.

A host of Wall Street banks are underwriting Facebook's offering, with Morgan Stanley, JPMorgan and Goldman Sachs serving as leads. Facebook will trade on Nasdaq under the symbol FB.