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Shares of e-commerce site Groupon Inc. (NASDAQ:GRPN) fell more than 10 percent Monday, giving back about half their Friday gains on speculation the troubled shopping site might be acquired.

At the close, shares of Chicago-based Groupon were down 43 cents to $4.25, down 9 percent, after setting a three-month high of $4.68 on Friday, when they soared 23 percent. Analysts, such as Tom Telsey of Forte Advisory, suggested the company may be attractive to Google (NASDAQ:GOOG), the No. 1 search engine.

Last Thursday, Eric Best, CEO of Mercent Group, an e-commerce specialist, said Google Shopping has seen gains of 65 percent over last year's holiday season. Groupon specializes in matching consumers with daily deals.

A year ago, before Groupon's much-delayed initial public offering, Google expressed interest in the site. But Groupon CEO Andrew Mason and its venture capital investors preferred to conclude the IPO.

Since then, shares of Groupon had slid 80 percent through Thursday, lowering the company's market value to only $3 billion. That declined to $2.97 billion on Monday.

Mason survived a directors meeting on Nov. 30 at which he was expected to be ousted due to the share decline as well as its lack of profit in three of the last four quarters.

Neither Groupon nor Google issued comments Friday or Monday. Shares of Google rose $1.21 to $685.42 on Monday.