When confronted at a golf tournament in Ohio last month, Mr. Mickelson instructed F.B.I. agents to "speak to my lawyers," according to a nearby observer.
Mr. Mickelson has hired Gregory B. Craig, a partner at the law firm Skadden, Arps, Slate, Meagher & Flom who was previously White House counsel under President Obama.
Several former federal prosecutors who worked on insider trading investigations, speaking on the condition of anonymity to avoid antagonizing law enforcement officials, questioned the decision to approach Mr. Mickelson after he finished a round of golf at the Memorial Tournament in Dublin, Ohio. The former prosecutors speculated that the government wanted to embarrass him into cooperating against Mr. Walters.
"If this were the only effort they made at that time to contact him, having it be so public could be seen as an aggressive move," said Daniel C. Richman, a criminal law professor at the Columbia University School of Law.
Mr. Mickelson, Mr. Icahn and Mr. Walters have issued statements denying any wrongdoing. Mr. Mickelson, who said he has "done absolutely nothing wrong," added "I'll cooperate as much as I can with the F.B.I." In an interview. Mr. Icahn said, "I don't give out inside information," adding that "for 50 years I have had an unblemished record."
Richard Wright, a lawyer for Mr. Walters, said his client had not had any contact with the authorities about his trading activity. Mr. Wright said no one from the F.B.I., the S.E.C. or the Justice Department had reached out to Mr. Walters, who is known to be an active stock trader, either before or after the investigation became public.
Mr. Icahn similarly has not received any subpoenas from the authorities, a person briefed on the matter said.
The lack of subpoenas struck some former prosecutors as odd. Once the investigation became public, the former prosecutors said, they would have anticipated authorities sending out subpoenas seeking access to emails and other records. Such documents would most likely be needed to help establish that Mr. Walters and Mr. Mickelson had traded stocks while in possession of inside information.
And even if Mr. Icahn did share secret information about his firm's Clorox intentions, he may have done so legally. It would be illegal if he breached a duty of confidentiality to his own investors.
Any suspicion that the three — Mr. Mickelson, Mr. Icahn and Mr. Walters — formed a triangle of insider trading has failed to materialize. Nothing in the public record suggests Mr. Icahn and Mr. Mickelson even know each other. Mr. Icahn and Mr. Walters both have acknowledged knowing each other — people who know them say the two men have wagered on sporting events together. But both Mr. Icahn and Mr. Walters insist they have never shared inside information.
Mr. Mickelson and Mr. Walters have participated in golf tournaments together. And outside the world of sports gambling, Mr. Walters, better known as Billy, is a prominent Las Vegas figure as the owner of popular golf courses.
It is unclear why federal authorities initially suspected that Mr. Mickelson may have played a role in the Clorox trades. The S.E.C. began the inquiry into Clorox trading after finding suspicious trades in the stock just days before Mr. Icahn's unsolicited bid.