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March 19 (Reuters) - Cloud storage company Dropbox Inc'sinitial public offering was oversubscribed, two peoplefamiliar with the matter said on Monday, indicating healthydemand for the first big tech IPO this year even as tech stocksopened the week on sour note.

While investor appetite looked encouraging with three daysto go before final pricing, it was not clear if that would bestrong enough to lift the deal above of the initial range of $16to $18 a share that Dropbox set last week. The offering isexpected to price Thursday, and the stock will start trading onthe Nasdaq on Friday.

"It is early to predict the pricing. But what I can say isthat from the conversations it seems the market is interested init and IPO seems to be bright," a separate source told Reuters.The three sources asked not to be named as the IPO pricingprocess was still underway.

Dropbox's IPO comes in what is sizing up to be a challengingweek for stocks, with the U.S. Federal Reserve set to raiseinterest rates on Wednesday, a day before the Dropbox deal isset to close.

Tech shares also fell hard to open the week, with Nasdaqdown more than 2 percent on reports of Facebook Inc'slatest data privacy problems.

Dropbox's IPO also comes on the heels of an upsized deallast week from cyber security firm Zscaler Incand is being watched as a barometer of investorenthusiasm for tech unicorns - young companies valued at morethan $1 billion - after Snapchat owner Snap Inc'sshares cratered following a much-touted IPO a year ago.

Dropbox and existing stockholders are selling 36 millionshares, and the offering could be increased by 5.4 million ifunderwriters exercise their right to buy more stock. At the highend of the indicated pricing, it could raise nearly $650million, making it the largest tech IPO since Snap hit themarket just over a year ago.

"The book is oversubscribed, with very good quality," one ofthe sources said.

The current price range suggests the San Francisco company,co-founded in 2007 by Andrew Houston and Arash Ferdowsi, willhit the public market valued at roughly $7 billion, a heftydiscount to the $10 billion implied by its last funding round in2014.

Houston is the largest shareholder and will retain 24percent of Dropbox after selling 2.3 million shares in theoffering. Sequoia Capital is the largest shareholder amongoutside investors, with about a 25 percent stake.

The company has 500 million users and competes with AlphabetInc's Google, Microsoft Corp, Amazon.com Incand has Box Inc as its main rival.(Reporting by Sweta Singh, Nikhil Subba and Diptendu Lahiri inBengaluru, Editing by Dan Burns and Saumyadeb Chakrabarty)