The newspaper reported the discussions were preliminary and could break down.
Under the plan, HP would at first own a minority interest in CSC, the newspaper said, adding that the computer maker could buy out Blackstone and other private-equity owners at a later date.
The Journal said it was unclear what Blackstone and HP would pay for CSC, but added that people familiar with the matter said, which would amount to about $12 billion.
Shares ofclosed at $50.82 on the New York Stock Exchange on Wednesday.
Representatives of CSC, Blackstone and HP could not be immediately reached for comment.