Reuters cited sources familiar with the matter as saying the acquisition talks were in an advanced stage.
If the deal does eventuate, it would be the second case where a big chip vendor dips its toes in the field of security.
Intel bought McAfee in 2011 but failed to gain a foothold in the security arena. It then sold a majority stake to the investment firm TPG.
Last year, Broadcom attempted to buy Qualcomm but the deal was scuttled by US President Donald Trump.
The then Singapore-based Broadcom was told it could not complete what would have been the biggest technology deal ever because of national security concerns.
Trump said he had made his decision based on a CFIUS review which had examined how Broadcom’s purchase of Qualcomm might affect 5G networks.
Symantec is being investigated by the Securities and Exchange Commission over accounting irregularities and also faces a lawsuit from shareholder James Felix, who claims its top executives massaged financial figures.
The company lost its president and chief executive Greg Clark in May, when he became the fifth top executive to quit in five months.
Clark's exit came after Symantec, one of the bigger security firms in the US, reported poor sales for the fourth quarter of fiscal 2019, though profits were bolstered by expenses being cut.