The meetings, which took place on March 7 and 8, will be disclosed in Dell's proxy statement on Friday and indicate Blackstone explored early on the possibility of keeping Michael Dell as CEO in a bid to take over the company, the person said on condition of anonymity because the information was not yet public.
Michael Dell also met this week with Blackstone's senior managing directors Dave Johnson and Chinh Chu, although the outcome of these discussions has yet to become clear, the person added.
Blackstone and Dell declined to comment.
The company set up a special committee to evaluate all options for the world's No. 3 PC maker, a move to placate concerns over potential conflicts of interest facing Michael Dell. The CEO owns 15.7 percent of the company he started in 1984 out of his college dorm room with $1,000.
Following a 45-day go-shop period that expired last week, Dell received two alternative preliminary takeover offers that sought to top a $24.4 billion deal Dell had reached with its founder and buyout firm Silver Lake to go private.
One offer was from Blackstone, Francisco and Insight Venture Management and the other was from billionaire Carl Icahn, who has amassed a roughly $1 billion stake in the Round Rock, Texas-based company.
Icahn has proposed paying $15 per share for 58 percent of Dell. Blackstone has indicated it can pay more than $14.25 per share for the whole of the company, all in cash or partly in shares, thereby also leaving Dell as a publicly listed company. Silver Lake's $13.65 per share all-cash offer would see Dell go private.
Dell said on Monday that Blackstone's and Icahn's proposals could reasonably be expected to result in superior offers, and that it would continue negotiations with both parties to secure superior bids that are binding and financed.
Michael Dell has expressed concerns that Blackstone's offer would dismantle the PC maker he founded in 1984, two people close to Michael Dell familiar with the matter have previously told Reuters.
The founder is worried that the buyout firm's plans would be inconsistent with his strategy to reinvest in the company, the people added.
Blackstone has already made an unsuccessful push to recruit Oracle Corp President Mark Hurd to run Dell if it takes over the company, one source familiar with the situation said last week. (Also see: Dell takeover battle: All you need to know)
© Thomson Reuters 2013