A deal could value Prague-based Avast at more than $8 billion, The Wall Street Journal previously reported, citing sources familiar with the matter.
NortonLifeLock shares at last check were 4.5% lower at $25.69.
The deal might involve a mix of cash and stock, NortonLifeLock said. The Tempe, Ariz., company said there's no certainty that any transaction will take place.
NortonLifeLock said buying Avast would bring together two companies with "highly complementary business profiles."
U.K. rules require NortonLifeLock to firmly decide by Aug. 11 whether it will make an offer or not.
Cybersecurity stocks are a hot commodity amid multiple high-profile cyberattacks involving ransomware attacks.
Avast "should not settle for less than $10 billion," Berenberg said in a note Thursday, according to Reuters.
"We are in an age where even real, critical infrastructure is being targeted by cybercriminals, propelling valuations in the cybersecurity industry. Moreover, with private equity and large enterprises attempting to outbid each other, deal premiums have gone up.”
Avast's founders sit on the company's board and control about 35% of the shares. Activist investor Starboard Value LP also has a stake in Norton and holds a board seat.
In May, NortonLifeLock shares rose after it drew analyst plaudits for its stronger-than-expected fiscal-fourth-quarter earnings.
Profit for the quarter ended April 2 registered $194 million, or 33 cents a share, down from $231 million, or 36 cents, a year earlier. Analysts surveyed by FactSet expected 30 cents for the latest quarter.
NortonLifeLock reported revenue of $672 million in the quarter, up 9% from $614 million a year earlier. The analyst consensus called for $660.2 million in the latest quarter.