In a letter to the company, Icahn said he would put the company through "years of litigation" if the board did accept the proposal and then, if the proposal was rejected, did not allow a vote on the privatization sale at its next annual shareholder meeting.
Dell's founder Michael Dell has spearheaded an effort to take the company private in a $24.4 billion deal that several major shareholders have said undervalues the company.
The $24.4 billion amounts to a sale with a per share value of $13.65.
Icahn's deal puts a "stub" value of each share at $13.81. Combined with the $9 per share dividend, Icahn's considers each share's true value to be $22.81.
"We have spent a great deal of time and effort in determining the $22.81 per share value and would pleased to meet with you to share our analysis and to understand why you disagree, if you do," the letter to the company says.
The Wall Street Journal reported Thursday that Icahn owns 6 percent of Dell. He is the company's second largest shareholder after Michael Dell.
The company said it was focused on a "go-shop" process, which is a time period, which ends March 22, in which it hunts around for a better deal than the $24.4 billion deal put together by its founder.