Activist investor Carl Icahn and Southeastern Asset Management Inc, two of Dell biggest shareholders, have proposed an alternative to a $24.4bn buyout deal led by founder Michael Dell.
Dell employs 2,000 people in Ireland at sites in Limerick and Dublin.
In a letter to Dell's board on Thursday night, Mr Icahn and Southeastern proposed that current owners keep their equity position. Additionally, they would have the option of receiving a distribution of $12 a share in cash or $12 a share in stock valued at $1.65 a share.
The proposal is the latest twist in the saga involving the future of one of the world's largest personal computer makers, once a high flyer now struggling to evolve as people embrace smartphones and tablet computers.
Michael Dell and private equity firm Silver Lake want to take the company private for $13.65 per share, making it the largest private equity-led buyout since the 2008 financial crisis.
Dell shares rose 0.5pc to $13.39 in early Friday trade.
Mr Icahn and Southeastern said in the letter it was "insulting to shareholders' intelligence for the board to tell them that this board only has the best interests of shareholders at heart. We are often cynical about corporate boards but this Board has brought that cynicism to new heights".
Dell said in a statement that the special committee of the Dell board was reviewing the Southeastern Asset materials and would provide comment in "due course." A representative for Silver Lake declined to comment.
"I don't think Icahn and Southeastern have enough sway over the shareholders," Raymond James analyst Brian Alexander said.
"As Dell has a lot of cash, (the latest deal) is basically like a leveraged private equity deal, without the company going private."
Icahn and Southeastern said if Dell's board pursued the go-private offer with a shareholder vote, they would put up a slate of 12 directors to challenge the current board. Both Mr Icahn and Southeastern said they would take additional shares rather than cash. They would finance the proposal from existing cash and about $5.2bn in new debt.
Mr Icahn and Southeastern together hold about 13pc of Dell stock.
Mr Icahn has previously proposed paying $15 per share for 58pc of Dell.
In April, Blackstone LP ended its pursuit of Dell, pulled out a month after it teamed up with Icahn to challenge the take-private attempt. (Reuters)