Michael Dell and Silver Lake Management LLC won’t sweeten their $24.4 billion offer to take Dell Inc. private, people with direct knowledge of the situation said.

Dell and Silver Lake are ruling out an increase because the $13.65-a-share offer they made in February represents a fair and significant premium to where the stock would trade if the deal fell apart, said one of the people, who asked not to be identified because the process is private.

The decision is the latest in the fight over Dell, set to culminate in a shareholder vote on July 18. While Institutional Shareholder Services Inc. is leaning toward a negative recommendation on Michael Dell’s proposal, people familiar with the situation have said that billionaire Carl Icahn said this week that he secured $5.2 billion in debt financing to support his third and last attempt to scuttle the leveraged buyout, or LBO.

“Michael can refuse to budge because even if shareholders vote down his offer, he and any special committee can and will make it tough for Icahn to get an alternative proposal approved,” said Erik Gordon, a business professor at the University of Michigan. “The downside to Michael of a defeat is small — his status at Dell would remain just as is it was before he made his bid.”

Michael Dell and Silver Lake decided not to increase their offer after being encouraged to do so by the special committee of Dell’s board, according to the people familiar with the situation. Silver Lake is willing to walk away from the deal if the bid isn’t successful, and Michael Dell isn’t prepared to finance personally another price increase as the company’s core PC market continues to deteriorate, said one of the people.

Representatives for Dell and Silver Lake declined to comment.

The special committee already negotiated six price increases before agreeing to the buyout announced on Feb. 5, a March 29 proxy filing shows. Michael Dell personally financed the last and final price increase with $500 million in cash and by committing to roll over 273.3 million shares at $13.36 apiece.

Icahn, Dell’s second-largest shareholder with an 8.7 percent stake, is proposing that the company make a tender offer for about 1.1 billion shares at $14 apiece. The activist investor said the buyback would address two shortcomings of the LBO offer: that it’s too cheap and that it doesn’t give shareholders the opportunity to profit from any improvement in Dell’s performance.

Michael Dell, who founded the PC maker 29 years ago, believes he can keep control of the company in the long run even if he fails to take the company private, said a person familiar with his thinking. Dell calculated he would keep control of the company even if Icahn succeeded because his stake would grow to about 41 percent if he didn’t tender to Icahn’s proposal, who would have about a 22 percent stake, the person said.

While the success of the founder’s buyout proposal requires approval by a majority of shareholders, excluding Michael Dell, who has a 15.6 percent stake, Icahn’s plans could succeed only after shareholders vote against the buyout and eventually give him control of the board in a so-called proxy fight in which Michael Dell can and will vote.

Icahn’s proposal would add substantial debt, decrease financial flexibility and “hurt the company’s ability to weather an economic or business downturn,” Michael Dell said in a June 21 regulatory filing. “It would also jeopardize customer perception and employee retention.” He wants to take the company private to implement a turnaround to adapt it to new trends such as cloud computing, which in the short term would worsen the company’s earnings and margins.

Dell’s special committee, which last month urged shareholders to vote for Michael Dell’s buyout, said Friday in a regulatory filing that Icahn’s tender offer gives the personal- computer maker a valuation more than twice that of its closest peer, Hewlett-Packard Co., and isn’t based on a concrete cost- savings plan. There’s a “substantial downside risk” to shareholders if they reject Michael Dell’s transaction, according to the filing.

Michael Dell expects the stock to fall to about $7.90 a share, based on trailing earnings, if the LBO is voted down, according to a person with direct knowledge of his thinking.