Several large Dell shareholders, who collectively own more than 5 percent of the company, told Reuters that they believed the $13.65 per share bid by founder Michael Dell and private equity firm Silver Lake Partners to take Dell private would fall through unless the terms were improved.

The investors said they told the board that the bidders would need to increase the price or offer shareholders a chance to continue to own a piece of the company for them to approve the deal. Failing that, the investors said, they want the board to come up with a 'Plan B' for Dell.

"Almost anything is an improvement from what they have offered," said Don Yacktman, president of Yacktman Asset Management, whose fund owns 14.9 million shares of Dell and has previously said he would vote against the current offer.

"I think if he were to go over $15, he would have success," Yacktman said, referring to Michael Dell.

A Dell spokesman declined to comment. Representatives of Michael Dell and Silver Lake also declined to comment.

The shareholder pressure on Dell comes ahead of a key report expected next week by investment advisory firm Institutional Shareholder Services, and a July 18 shareholder meeting, when investors will vote on the Michael Dell-Silver Lake deal.

Although it is still too early to call the results of the vote, early indications point to increasing opposition from investors.

The Dell board's special committee, which is overseeing the process, is also reviewing a competing plan floated by billionaire investor Carl Icahn, who wants the company to buy back 1.1 billion shares at $14 apiece. Icahn made progress with that proposal, disclosing on Tuesday that he had committed more than $3 billion to back his plan.

Dell investors fear that if Michael Dell's current bid fails, it will be followed by a precipitous drop in the company's shares unless the company comes up with a credible alternative.

Dell has struggled to deal with a declining global PC market, which is reeling as tablets gain in popularity. Dell has been trying to transform into a provider of enterprise computing services but has met with limited success.

Shares of Dell closed down 0.5 percent at $13.31 on Wednesday, slightly below $13.65, indicating investors expect the worst case scenario will be avoided.

(Reporting by Soyoung Kim, Jessica Toonkel and Nadia Damouni in New York; Editing by Diane Craft)

By Soyoung Kim, Jessica Toonkel and Nadia Damouni