The No. 2 U.S. personal computer maker is the unidentified company mentioned in a statement made by Quest, which disclosed on Thursday that it had received an offer from a "strategic bidder" of $25.50 per share - a 7 percent premium to Quest's Wednesday close of $23.86.

Dell is being advised by Bank of America Merrill Lynch, two of the sources said.

Quest's shares rose more than 9 percent to finish at $26.06 on Thursday.

Dell has been actively buying companies to expand its offerings to business and diversify away from personal computers, a market whose growth is decelerating as Apple Inc's iPad and other mobile devices pull customers away.

This week, it told investors its focus on the hardware and software needs of corporate customers was gaining momentum. Quest could shore up Dell's businesses in data management and protection and Windows server management.

On-again, off-again talks between Dell and Quest had broken off last month. The PC maker at that time was planning to offer between $23 and $26 per share to buy the software maker.

Dell, Quest and Bank of America declined to comment. Insight was not available for comment

On Tuesday, Chief Executive Michael Dell told analysts that his software business remained "modest" and was one area where he could envision his company growing rapidly.

Quest -- which makes software to monitor the flow of data through networks -- has worked with Dell since 2004 and is one of the PC maker's top 10 partners. Dell ranks among Quest's five largest partners.

THREE DAYS TO RESPOND

Quest agreed to be bought by Insight for $23 per share in March, but it also cast around for a better offer.

Insight would have the right to match rival offers, or adjust its own bid. The venture capital investment firm now has three days to respond on the offer, Quest said on Thursday.

If Quest were to strike a new deal, it would have to pay Insight a break-up fee of either $4.2 million or $6.3 million, depending on the timing of the deal.

"It's a very small breakup provision," Wunderlich Securities Inc analyst Brian Freed said, adding that it was "recognition by management that there were likely other buyers at higher levels."

Aliso Viejo, California-based Quest is led by Chief Executive Vinny Smith, who has served as either chairman or the CEO for more than a decade.

Any deal with Quest is fraught with complications as roughly 34 percent of Quest is owned by Smith, who took over in February after Doug Garn stepped down, citing poor health.

Big companies can bid aggressively for smaller ones with key technology, as was the case when Dell and Hewlett-Packard Co got into a bidding war for data storage company 3Par Inc in 2010. Dell spurred that fight with an $18-a-share bid, but HP ended up buying the company for $33 a share.

And there may be a lot of upside left in Quest's price.

"The offer from Insight was in the bottom 10 pct in the valuation range for software companies in the sector over the last two years," Freed said.

(Reporting By Poornima Gupta in San Francisco, Nadia Damouni in New York. Additional reporting by Supantha Mukherjee and Sruthi Ramakrishnan in Bangalore and Luisa Beltran in New York; Editing by Supriya Kurane, Anthony Kurian, Saumyadeb Chakrabarty)

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