Icahn, who owns a nearly 9 per cent stake in Dell, now wants shareholders to receive warrants in addition to the cash he previously recommended be given to shareholders.
Icahn previously proposed that Dell "self-tender" 1.1 billion shares of its stock for $14 per share. His revised proposal adds one warrant for every four shares. The warrant would give shareholders the right to buy one Dell share for $20 over the next seven years. Dell's shares haven't traded above $20 since September 2008.
In a letter to shareholders, Icahn values his counterproposal at about $15.50 to $18 per share.
Meanwhile, Michael Dell and Silver Lake Partners have offered to buy the entire company for $13.65 per share. Shareholders are set to vote on that offer at a meeting Thursday.
But Icahn argues that Michael Dell's offer undervalues the company and earlier this week asked a judge to assess its fairness.
The activist investor has proposed a variety of alternatives to keep the company publicly traded, but none have swayed the board from its support of the deal with Michael Dell and Silver Lake. What's more, Dell's board says its representatives contacted more than 70 potential suitors without finding any willing to ante up more than $24.4 billion.
In a late Friday statement, Dell's special board committee overseeing the company's sale said it's reviewing the merits of Icahn's latest offer. For now, the committee is still recommending that shareholders accept the offer from Michael Dell and Silver Lake.
"We have been and remain willing to meet or talk with Mr. Icahn about his various proposals, including at a meeting scheduled earlier this week which he requested and subsequently cancelled," the board said.
Round Rock, Texas-based Dell that has fallen on hard times as more consumers and companies buy smartphones and tablets instead of laptop and desktop computers.
Michael Dell is betting that he will be able to revive the company that he founded in 1984 by cutting costs, overhauling the sales force and diversifying into more profitable technology niches, such as business software, data storage and analysis and consulting services. The changes are likely to lower Dell's earnings, the main reason that Michael Dell wants to engineer the turnaround away from the financial pressures of Wall Street.
Dell shares slipped 3 cents to close at $13.32 Friday.