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Shares of Dell rose nearly 13 percent Monday after Bloomberg News reported the personal-computer maker was in talks with at least two private-equity firms about going private.

A buyout of Dell would be worth more than $17 billion, based on its total enterprise value.

The company has some $9 billion in debt, but $11 billion in cash at hand.

A deal would make it the largest technology buyout since the $17.6 billion acquisition of Freescale Semiconductor by a group of buyers led by the Blackstone Group in 2006.

The Bloomberg report, citing two people with knowledge of the matter, said the talks were preliminary. It cautioned that the firms might not be able to line up financing.

The report of the talks comes a week after a top Dell executive, David Johnson, who was in charge of corporate strategy including deals, left to join Blackstone.

Any buyout would involve Michael Dell, who started the company out of his University of Texas dormitory room in 1984. The chief executive owns nearly 16 percent of the company.

At a Sanford C. Bernstein conference in June 2010, Dell was asked whether he had considered taking the private. “Yes,” was all he would say.

Since Dell returned as chief executive six years ago, the company has tried to move from its core business of PCs and computer servers into the more stable and growing business of equipping corporate data centers with hardware and software. Its PC and associated laptop businesses, however, still account for about half of Dell’s revenue.

That PC business is shrinking fast.

On Monday, Gartner, a market-analysis firm, said that for all of 2012 Dell sold 37.6 million PCs worldwide, a 12.3 percent drop from its 2011 shipments. It was the worst performance, in a weak market, of any major manufacturer.

Dell’s drop was particularly severe in both the United States and in the fourth quarter, indicating its erosion is accelerating.

Dell has been trying to cut its reliance on the PC business, but the company faces challenges.

The math for a leveraged buyout seems daunting, at least initially.

Dell’s market value as of Friday was about $18.9 billion. Assuming a 30 percent takeover premium — slightly below the average for high technology LBOs last year, according to Thomson Reuters — that would value the company at about $24.6 billion.