Wall Street Journal reported on Friday, citing people familiar with the matter.
The deal could be announced on Monday, although the talks could still fall apart, the report said.
McAfee and Advent did not immediately respond to Reuters requests for comment.
The potential deal comes at a time when the pandemic-driven shift to remote working and a rise in cyber attacks has spurred demand for antivirus and digital security software.
Seeking to create a leader in consumer security software, US-based NortonLifeLock Inc in August agreed to buy London-listed rival Avast Plc for up to $8.6 billion.
Shares of McAfee, which made its market debut last year, closed 20% higher on Friday at $25.46.
The company said in March it would sell its enterprise business to a consortium led by Symphony Technology Group for $4 billion in cash.
