The inquiry is reportedly examining whether Phil Mickelson and William Walters may have traded shares illegally, based on information provided by Carl Icahn.
Phil Mickelson’s lawyers say he is not the target of an investigation.
Carl Icahn, 78, denies giving insider information. William Walters has not yet commented.
Phil Mickelson, 43, has won five major championships and is one of the US’s highest-paid sportsmen.
The FBI, along with the Securities and Exchange Commission and federal prosecutors in Manhattan, are said to be looking into trading in two different stocks.
The investigation, which began three years ago, is focusing on trades in cleaning products company Clorox.
Carl Icahn, a billionaire investor and prominent activist, was mounting a takeover bid for Clorox around the time that Phil Mickelson and William Walters placed their trades, the New York Times reports.
“We do not know of any investigation,” Carl Icahn told Reuters news agency, saying he was proud of his 50-year “unblemished record”.
Investigators are also reportedly looking into trades that Phil Mickelson, a three-time Masters champion, and William Walters made relating to Dean Foods, the Wall Street Journal reports.
The New York Times quotes sources saying federal authorities are looking into trades placed in August 2012 just before the company announced quarterly results.
Those trades appeared to have no connection to Carl Icahn, the newspaper added.
The FBI and other federal agencies have not commented publicly on the allegations.
None of the men have been directly accused of any wrongdoing.
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