Michael Dell, founder of the company, has teamed up with equity firm Silver Lake to create a $24.4 offer to take Dell private.
Dell has said the computer market is moving from personal computers to mobile devices and that it would be easier to retool the company to adapt to the changing marketplace if it were taken private.
Dell's board, after considering other options, decided to put the founder's offer up to a shareholder vote.
The Wall Street Journal reported Friday that Icahn has tweaked his offer by adding a warrant option, which is an agreement to buy stocks in the future at a set price.
Icahn's offer includes having the company issue a tender offer for 1.1 billion shares priced at $14 each. On top of that, his new deal includes a warrant for every four shares tendered. That would, under certain conditions, allow shareholders to buy shares at $20 per share in the future.
Shareholders are set to vote on Dell's option on July 18, the Journal said.
Dell's plan has received backing from several investment advisory firms, including International Shareholder Service Inc., which studied the options and decided, essentially, if the founder of the company was willing to stick his neck out and accept all the risk for the company then there should be an acceptable price somewhere for such an option.
"From a public company shareholder's perspective, if your chief executive officer is willing to buy your falling knife for the privilege of catching it, there is probably a price at which you should let him," ISS said.