The company said the committee has determined that the bids from buyout specialist Blackstone and Icahn could be superior to a proposal from CEO Michael Dell and Silver Lake Partners to buy the company for $13.65 a share.
Blackstone proposed buying the company in a deal that would equate to more than $14.25 a share. Icahn wants to buy up to 58 percent of Dell's shares for $15 each.
The company said Michael Dell, who founded the company, is willing to work with third parties on alternate acquisition proposals.
Dell Inc. (DELL) shares climbed 3.3 percent, or 47 cents, to $14.60 about 70 minutes before markets open on Monday.
Silver Lake Partners raised its bid six times by about $4 billion over the course of negotiations, and the committee still recommends that bid while it evaluates the other offers, according to a statement from the company. But Icahn and other investors have criticized that bid as too low.
Southeastern Asset Management, Dell's second-largest shareholder after Michael Dell, has asserted the company is worth closer to $24 a share.
The offer from Michael Dell and Silver Lake was announced in early February. Dell's board then set a 45-day period to allow for offers that might top that bid. That period expired Friday.
Many investors expected that a higher bid was in the works for the world's third-largest PC maker. Several buyout scenarios tying Blackstone to Dell were leaked to the media last week.
Dell and other PC makers are struggling as technology spending shifts to smartphones and tablet computers. Dell and HP, the top PC maker, are trying to adapt by making more tablets and diversifying into more profitable areas of technology, such as business software, data analytics and storage.
Michael Dell believes he will be in a better position to overhaul the company if he no longer has to worry about Wall Street's focus on profit fluctuations from one quarter to the next.
Shares of Dell had climbed nearly 40 percent so far in 2013, as of Friday's market close. That includes a rise of nearly 7 percent since the shares closed at $13.27 on Feb. 4, the day before the Dell-Silver Lake bid was announced.