Quest Software Inc. has received an improved bid from Dell Inc to buy the maker of enterprise management software for about $2.32-billion (U.S.) a source close to the matter said on Monday.

Two bidders have recently been competing to buy Quest: a buyout group led by private investment firm Insight Venture Partners, and an undisclosed bidder.

On Monday, a source close to the matter told Reuters that the mystery bidder was actually Dell. Quest disclosed on Monday that it had received an improved bid of $27.50 per share in cash from the mystery bidder, but did not reveal the bidder's identity.

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Reuters reported on May 25 that Dell planned to offer $23 to $26 per share to buy Quest. The source who spoke to Reuters on Monday requested anonymity because the takeover talks are private.

Dell declined to comment on Monday, and a Quest representative was not immediately available for comment.

Dell's offer beats an earlier bid of nearly $2.17-billion or $25.75 a share from the Insight Venture Partners buyout group which includes Vector Capital.

Shares of Quest were up 5.3 per cent at $27.61 on Monday morning on the Nasdaq, suggesting that investors expect a counter-offer to emerge.

Quest said its board of directors has determined the new proposal is superior to prior offers.

Last week, Quest agreed to sell itself to Insight for $25.75 per share, after the private investment firm and new partner Vector Capital raised their bid.

The Insight-Vector cash offer of $25.75 a share had topped a $25.50 bid made by a "strategic bidder" that Reuters later identified as Dell.

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The terms of the agreement, not including the price, are similar to the original proposal from Dell, including no financing conditions and paying the bidder a breakup fee of 3.5 percent.

Insight would have the right to match rival offers, or adjust its own bid. The venture capital investment firm has three days to respond on the offer, according to terms in the merger agreement.

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

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

Major tech companies have often preferred to keep their identities private when bidding wars start to heat up. This helps prevent the bidder from feeling compelled to overpay and also spares it the public embarrassment of an unsuccessful takeover attempt.

One of the last public battles was when Dell fiercely competed against Hewlett-Packard Co. for data storage company 3Par Inc in 2010.

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Dell spurred that fight with an $18-a-share bid, but HP ended up buying the company for $33 a share.

On-again, off-again talks between Dell and Quest had broken off last month, sources have said. Dell has yet to publicly acknowledge any interest in buying Quest.