It was not clear why Blackstone, which has been negotiating with potential partners to make a play for the PC maker, decided to pull out. Billionaire Carl Icahn has also taken a significant stake in the company and opposes Michael Dell's effort.
Activist investor Icahn and Blackstone have each offered alternatives that would keep part of the company public, although they have also held preliminary talks about working together.
Icahn has proposed paying $15 per share for 58 percent of Dell, while Blackstone has indicated it could pay more than $14.25 per share. Both deals involve saddling the company with a good deal of debt and keeping it on public markets. Silver Lake's $13.65 per share all-cash offer would see Dell go private.
Blackstone and Silver Lake declined to comment. Dell could not be reached immediately for comment outside of regular U.S. business hours.
Dell was regarded as a model of innovation as recently as the early 2000s but has struggled to make up for a declining share of the global PC market. The company is now trying to transform itself into a provider of enterprise computing services, reducing its reliance on PC sales.