Broadcom is in discussions to pay about $140 per share in cash and stock for VMware, the sources said. That is a 46% premium to the value of VMware's shares on Friday.
If the negotiations prove successful, a deal could be announced as early as Thursday, when VMware is scheduled to report quarterly earnings, the sources added.
Bloomberg News first reported the deal talks on Sunday, while the Wall Street Journal first reported on the acquisition terms on Monday. Broadcom and VMware did not immediately respond to Reuters' requests for comment.
VMware shares ended trading on Monday up 25% at $119.43, while Broadcom shares closed down 3% at $526.36.
Broadcom makes an array of chips used in products ranging from mobile phones to telecom networks. The acquisition of VMware would give it access to data centers where the latter's technology is a mainstay for cloud customers.
"We believe an acquisition of VMware would be considered as making strategic sense; consistent with Broadcom's focus on building out a deepening enterprise infrastructure software strategy," Wells Fargo analysts said.
Broadcom Chief Executive Officer Hock Tan, a Malaysian-American billionaire, has been a prolific deal maker since taking the helm of what was a small chipmaker in 2006. Regular acquisitions helped turn the business into a behemoth worth more than $200 billion.
Tan's most audacious move was to try to buy mobile chipmaker Qualcomm for $103 billion in 2017. That was blocked by U.S. President Donald Trump over concerns that it would give China the upper hand in mobile communications.
After the failed effort, Broadcom moved its headquarters to San Jose from Singapore. It subsequently beefed up its software offering by buying CA Technologies for $18.9 billion and Symantec's security division for $10.7 billion.
"A VMware acquisition would just about triple the size of Broadcom's software segment, as well as bring the overall software mix close to 50% for the combined company," Bernstein analysts wrote in a note to clients.
Michael Dell is VMware's biggest investor with a 40% stake after the company was spun out of Dell Technologies last year. Private equity firm Silver Lake, which has previously invested in Broadcom, is VMware's second largest shareholder with a 10% stake.
TIMELINE-Broadcom's deal history under CEO Hock Tan
(Reporting by Greg Roumeliotis in New York, Shivam Patel in Bengaluru and Supantha Mukherjee in Stockholm; Editing by Christian Schmollinger, Tom Hogue, Kirsten Donovan and Bernard Orr)
By Greg Roumeliotis and Supantha Mukherjee