"They've been very clear about their intention to continue to hold, and they're very committed to the investment," Dell told CNBC's "Squawk on the Street" Monday. "I tell you, I've asked them several times, 'Hey, you guys want to sell?' I'll buy them out."
Dell Technologies announced Monday it will buy out the holders of shares that track the performance of VMware using a mix of cash and equity in Dell. The move means Dell will again trade on the stock market, about five years after the private equity firm Silver Lake and Michael Dell teamed up on a $24.9 billion deal to take the technology company private.
"In the last five years a lot has changed. We've completely transformed the business, become the essential infrastructure company, really changed the profile nature of the company in terms of our capabilities," Dell said. "This was about simplifying our capital structure and exposing the value that we've created to shareholders."
Silver Lake owns about 18 percent of the company.
The tracking stock was introduced in 2016 to help Dell pay for its $67 billion purchase of EMC Corp. The new security was linked to part of EMC's interest in VMware, and the rest is publicly traded along with the tracking stock.
Dell has been conducting a strategic review for several months as it has sought to consolidate its complicated ownership structure without overburdening its balance sheet, which bears around $50 billion in debt.
Dell said it will propose to exchange each share of VMware tracking stock for 1.3665 shares of Dell Technologies Class C common stock, or at the holder's election, $109 in cash, subject to the total amount of cash consideration not above $9 billion.
The transaction represents a premium of 28.9 percent to Dell's closing price on Friday.
"There is a technology led boom in investment that requires modern IT infrastructure, and Dell Technologies is the lead infrastructure company on the planet," Dell said. "We've capture the hearts and minds of the decision-makers."
Shares of VMware rose nearly 10 percent.
The cash component of the offer will be financed by a one-time $11 billion special dividend that VMWare will pay out pro-rata to its shareholders, VMWare said.
After the deal, VMware shareholders would own between 20.8 percent to 31 percent of Dell, depending on how many investors opt for cash, Dell said.
Dell considered several other transactions since January, including going public and pursuing a reverse merger with VMware. Dell has wanted to simplify its capital structure, give its private holders a publicly traded currency and increase its ownership of VMware.
Back in May, Dell hinted at a stock deal with owners of DVMT, which has a market capitalization of about $17 billion.
—CNBC's Alex Sherman and Reuters contributed to this report.