The private equity group and billionaire investor Carl Icahn were both in the hunt for Dell, but Blackstone pulled out, The Wall Street Journal reported Friday.
Blackstone said it had had concerns about Dell's operating income and declining sales.
Dell founder Michael Dell offered to take the company private for $24.4 billion, explaining that might make a turnaround more easily handled.
That offer set up a bidding period, with the company board naming a special committee to review rival bids.
Dell is struggling to keep its momentum going after establishing itself as a leader in the personal computer business.
The computer industry is more diverse than it once was, with consumer choices now including a variety of mobile devices from phones to digital tablet readers to devices like the Ipod Touch.
Dell, once in the right place at the right time, does not want to be left in the dust as consumer trends change, analysts say.
Duggar sisters unveil Christian dating rules in new book
Attkisson leaves CBS News, reportedly over network's 'liberal bias'