Blackstone still has time because Dell is still within its go shop period. That's the window of time a public company has to find better offers than the original offer on the table. It usually lasts about one or two months.
Right now Dell (with the help of Microsoft and Silver Lake) is going private at $24.4 billion, or $13.65 a share, but some shareholders have said that the company is more valuable.
Maybe Blackstone will satisfy them.