A deal could be reached in weeks, Bloomberg reported, citing unnamed people familiar with the matter.
Symantec shares rose $4.90 to $27 in after-hours trading. Broadcom fell $12.08, or 4%, to $283.25.
A deal would follow Broadcom CEO Hock Tan's move last year to acquire CA Technologies, a move that followed his company's failed efforts to acquire Qualcomm Inc. (QCOM) . That acquisition was blocked by President Donald Trump on national security concerns.
Elsewhere in the cyber security sector, stocks were mixed Tuesday.
Among decliners, Carbonite shares (CARB) fell 80 cents, or 3.05%, to $25.47. Carbon Black shares (CBLK) fell 22 cents, or 1.29%, to $16.79. And FireEye shares (FEYE) fell 19 cents, or 1.28%, to $14.70.
The ETFMG Prime Cyber Security ETF (HACK) rose 17 cents, or 0.43%, to $40.10.
The First Trust NASDAQ Cybersecurity ETF ETF (CIBR) rose 24 cents, or 0.84%, to $28.87.
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