The Intel logo is displayed outside of the Intel headquarters in Santa Clara, Calif.

Private equity firm Thoma Bravo is in early discussions to acquire security software company McAfee from TPG and Intel for a significant premium over the company's 2016 $4.2 billion valuation, according to people familiar with the matter.

Talks may still fall apart and a deal announcement isn't expected soon, said the people, who asked not to be named because the discussions are private.

McAfee, founded by John McAfee in 1987, historically developed cybersecurity software for personal computers and servers, protecting users from malware and other viruses. This type of computer security prevented attacks on personal devices. More recently, it has expanded into mobile devices and cloud computing, which is where hackers have migrated.

The company was publicly traded until 2010, when Intel bought it for $7.6 billion. The chipmaker hoped to closely align its chips with McAfee's security technology. That vision didn't pan out for Intel, which took a haircut of more than $3 billion when it sold 51 percent of the business to TPG in a deal announced in 2016 at a valuation of $4.2 billion. Several months later, TPG brought on Thoma Bravo to make a minority investment.

TPG's majority ownership has helped transform the McAfee business in less than two years with add-on acquisitions. In January, McAfee closed its takeover of Skyhigh Networks, which helps companies monitor which cloud services employees are using. In March, McAfee also acquired Tunnelbear, which provides virtual private networks that protect data when using shared WiFi accounts.

Intel sees itself as purely a financial investor in McAfee now, according to one of the people. Still, Intel has participated in the recent value creation of the standalone McAfee by holding its minority stake and stands in line to recoup some of the lost value if the Thoma Bravo deal goes though. A deal would unify the ownership of McAfee and could put it in position to go public again, two of the people said.

Reuters reported in November that Thoma Bravo had approached Symantec with a takeover offer. A deal for McAfee would rule out a Symantec purchase, one of the people said.

Spokespeople for TPG and Intel declined to comment. A spokesman for Thoma Bravo did not immediately respond.

--CNBC's Jon Fortt contributed to this report.

Correction: When Intel sold its partial stake in McAfee to TPG in 2016, McAfee's total valuation in that transaction was $4.2 billion.