The company said the offers were from billionaire corporate raider Carl Icahn and investment fund Blackstone Group.
Both proposals “could reasonably be expected to result in superior proposals,” but further study is needed, Dell said in a statement.
Dell said its special committee, which had set a Friday deadline for offers, would continue negotiations on both offers.
“We are gratified by the success of our go-shop process that has yielded two alternative proposals with the potential to create additional value for Dell shareholders,” said special committee chairman Alex Mandl.
“We intend to work diligently with all three potential acquirers to ensure the best possible outcome for Dell shareholders, whichever transaction that may be.”
In February, Dell unveiled plans to go private in a $24.4 billion deal. The private equity buyout led by founder Dell, backed by equity investment firm Silver Lake, would give shareholders $13.65 per share.
Blackstone proposed a “leveraged recapitalization” which would offer existing shareholders $14.25 per share, but allow those who want to hold the shares to be able to do so. Under the deal, shares would remain publicly traded on the Nasdaq.
The Icahn offer would inject an additional $5 billion into Dell, paying $15 per share, allowing the company to remain publicly traded but under new control.
The initial offer led by Michael Dell would de-list the company from stock markets and could ease some pressure on Dell. The company is cash-rich but has seen profits slump as it tries to reduce dependence on the shrinking market for personal computers.