Federal investigators are pursuing a major insider-trading probe involving finance, gambling and sports, examining the trading of investor Carl Icahn, golfer Phil Mickelson and Las Vegas bettor William “Billy” Walters.

The Federal Bureau of Investigation and the Securities and Exchange Commission are examining whether Mr. Mickelson and Mr. Walters traded illicitly on nonpublic information from Mr. Icahn about his investments in public companies, people briefed on the probe said.

Investigators are examining whether over the past three years Mr. Icahn tipped Mr. Walters—famous in Las Vegas for his sports-betting acumen—about potentially market-moving investments by Mr. Icahn’s company.

The FBI and SEC are examining whether Mr. Walters on at least one occasion passed a tip on to Mr. Mickelson, these people said, and are studying the two men’s trading patterns.

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