Billionaire investor Carl Icahn, in a bid to force Michael Dell to sweeten his $24.4 billion buyout proposal for Dell Inc., said he’ll come up with a higher offer for the PC maker by Friday morning.

The new bid will be “vastly superior” to the founder’s offer, Icahn said Thursday on Bloomberg Television’s “Street Smart” with Trish Regan. “We’re going to come in and add into the package — which we think is superior already.”

Icahn, who holds an 8.7 percent stake in Dell, has been agitating for months to try to force Michael Dell and buyout partner Silver Lake Management LLC to sweeten their $13.65-a- share offer. His latest plan would offer Dell shareholders $14 or the ability to retain equity in a publicly traded portion of the company — rather than the buyout group’s deal that takes all the shares off the table for outside investors.

The increased offer will include a warrant, Icahn said.

“We think the warrant will be around $20, to buy the stock at $20, and we’re going to give the shareholders a piece of that warrant,” Icahn said in the interview. “We think that will make it definitely superior. We think, after talking to a number of shareholders, that this should win the day for us. But you can’t be sure obviously.”

This would be the fourth effort by Icahn to scuttle Dell’s buyout. In March, Icahn offered $15 a share in cash for as much as 58.1 percent of the stock. Then, in May, he teamed up with Southeastern Asset Management Inc. to offer investors $12 a share in cash or additional Dell stock while letting them retain stakes in a public company. Last month, he offered to help finance the last $14-a-share buyback proposal.

Shareholder Vote

Shareholders are set to vote on the Silver Lake-led offer next week, after an earlier effort by Icahn to block the deal in Delaware court failed. The court argued that Icahn’s offer can’t be superior to Michael Dell’s because it’s not a full takeover.

Proxy advisory firm Institutional Shareholder Services Inc. recommended Dell shareholders vote for the $24.4 billion buyout by Dell and Silver Lake. Glass, Lewis & Co., another shareholder adviser, also backed the buyout proposal. A vote will be held at Dell’s Round Rock, Texas, headquarters July 18.

“From a public company shareholder’s perspective, if your CEO 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 in its July 7 report.

In a letter to Dell shareholders, Icahn urged them to seek a higher price for their shares in court, by exercising so- called “appraisal” rights available to shareholders of companies incorporated in Delaware. An October closing date for the deal would give investors until December to decide whether they want Dell’s price or a court appraisal, he said.