In February, Dell founder Michael Dell and an investment group offered to take Dell private for $24.4 billion, about $13.65 per share.
The deal prompted Dell's board to open up bidding for 30 days to see if they could stir up a better offer for shareholders.
The Wall Street Journal said Icahn's proposal includes a $5 billion equity commitment, which means he would spend $2 billion for outstanding shares -- a $15 per share offer. He would also provide $2 billion in equity financing.
The rival bid lead by Blackstone Management Associates values the company at $14.25 per share.
That falls between the offer made by Dell and Icahn in value, but it includes the caveat that Dell's current shareholders would be granted an option of staying with the company.
Dell's argument included his claim the computer maker, once the world's largest, would have an easier time turning itself around if it were a private company.
The company has been struggling to keep up with the market, where consumers once devoted to personal computers are now spreading their technology spending across a wide range or mobile devices, including phones, portable tablets, laptop computers, game platforms and hand-held computers, like the iPod touch.
Personal computers now make up half of the company's revenue, but that is expected to decline. From the fourth quarter of 2011 to the same period of 2012, shipments of PCs dropped 4.9 percent.
PCs made up 19 percent less of the company's revenue in the fourth quarter than it did in the October to December period of 2011 and the impact of the shift pushed profits down 47 percent from the same period of 2011, the Journal said.