The withdrawal follows reservations expressed by Blackstone's private equity fund investors on the merits of the deal, and concerns that the stock market had already valued Dell fairly, people familiar with the matter said.
There were also concerns among Blackstone management about the ability to withdraw from a Dell investment profitably, they added. Dell shares last night closed at $13.95, valuing the group at $24.4 billion.
Blackstone's preliminary offer was made jointly with Insight Venture Partners and Francisco Partners, investment firms that specialize in technology companies. It came during a go-shop period after founder Michael Dell and Silver Lake Partners proposed to take the personal computer maker private at $13.65 a share.
Dell's special committee agreed to reimburse Blackstone for its work as it considered a formal bid, for up to $25 million. Morgan Stanley is advising Blackstone.
By dropping out, Blackstone will increase the likelihood that Mr Dell and Silver Lake might prevail in their attempt to take the company private.
(Read More: Dell Strikes Deal With Icahn to Stave Off Buyout)
However, hurdles remain. Dell shareholders, including Southeastern Asset Management, have opposed the move by Mr Dell and Silver Lake because it does not allow existing shareholders a way to participate in the upside of a turnround.
Also, Dell's special committee will still have to consider a proposal by activist investor Carl Icahn, which was made during the go-shop period. Mr Icahn offered to buy 58 per cent of the company for $15 a share. Earlier this week, he secured a detente with Dell that will let him talk to other investors but not increase his shareholding above 10 per cent.
Mr Icahn declined Dell's offer to reimburse his expenses if he dropped the threat of a proxy fight, saying he wanted to retain that option. Instead of Dell being taken private, Mr Icahn has also lobbied the company to pay a special cash dividend to shareholders.
Blackstone's interest in Dell was always seen as lukewarm by many bankers. It offered a minimum of $14.25 a share, and provided a structure that would have allowed some large shareholders to retain equity in a so-called public stub.
People familiar with Blackstone's thinking said other factors in its decision to abandon its bid were its lack of in-house technology expertise, and the amount of Dell cash that is held overseas.