A $6 billion offer would represent a 35 percent premium to the last closing price of Mellanox on Nasdaq, the Calcalist financial news website said.
Based in Yokneam, Israel, Mellanox makes chips and other hardware for data centre servers that power cloud computing.
Officials at Intel and Mellanox declined to comment.
In October, CNBC reported that Mellanox had hired a financial adviser to explore a sale after receiving takeover interest from at least two companies.
On Monday, Israeli Finance Minister Moshe Kahlon said Intel plans to invest $11 billion to expand its manufacturing operations in southern Israel.