The buyout consortium is negotiating taking Dell private at $13 to $14 per share, two of the people said. This translates into an equity valuation for the Round Rock, Texas-based company of between $22.6 billion and $24.4 billion.
Dell shares were up 2.5 percent at $13.57 in afternoon trading.
Michael Dell is expected to take majority ownership of the world's third-largest personal computer maker while Silver Lake and Microsoft Corp
The transaction is set to be finalized over the weekend and the timetable could still slip, the people cautioned, asking not to be named because the matter is not public.
The investment group, which held negotiations with Dell's camp in New York on Thursday, has secured up to $15 billion of debt financing to take Dell private from four investment banks -- Barclays
Barclays is also advising Silver Lake on the transaction, along with Perella Weinberg Partners, said two of the people. JPMorgan Chase & Co
Representatives for Dell, Microsoft, Silver Lake and Barclays declined to comment. Perella Weinberg could not be immediately reached for comment.
As part of the transaction, Michael Dell will contribute his existing stake of almost 16 percent in the company toward gaining majority ownership, sources close to the matter have said. The deal would mark the largest leveraged buyout since the global financial crisis.
Going private would allow Dell, which has been trying to become a one-stop shop for corporate technology needs as the PC market shrinks, to conduct that difficult makeover away from public scrutiny.
Dell has formed a special committee of its independent directors and hired Evercore Partners Inc