A deal is not imminent and may not come together, but if a transaction does happen, it is expected to be announced in December.
According to the report, the deal could value Mellanox at more than $100 per share.
Up to Tuesday’s close, Mellanox had a market capitalisation of $4.74 billion.
Shares of Mellanox rose 4.5 percent to $92.55, while Xilinx was down 1.2 percent at $84.92.
Xilinx makes field-programmable gate array (FPGA) chips that are in used in circuit boards in data centres that run search algorithms and artificial intelligence. Ross Freeman, the co-founder of Xilinx, invented the FPGA in 1984.
Mellanox, which has a market cap around $5 billion, sells networking hardware used in data centres, including Ethernet switches, where Cisco rules the market, and cables for connecting switches to other hardware. Buying the company would give Xilinx a broader array of products to sell into the data centre market.