Prosecutors said they learned about the incident while preparing for a hearing on Wednesday on claims of government misconduct by Walters' lawyers, who contend the probe was leaked to breathe life into it.
While Walters' lawyers have said U.S. District Judge Kevin Castel could impose a number of sanctions, prosecutors on Friday said the remedy available was to hold the agent in contempt of court.
The agent, who prosecutors said admitted to being a "significant source" for the newspapers, was not identified. Representatives for Manhattan U.S. Attorney Preet Bharara's office and the FBI declined to comment.
Walters' lawyer, Barry Berke, also declined comment. Eileen Murphy, a spokeswoman for The New York Times, declined comment. Representatives for The Wall Street Journal did not respond to requests for comment.
Walters, who has built a fortune as a sports bettor, was arrested in May on charges that he traded on tips supplied by Thomas Davis, the former chairman of Dean Foods, who has pleaded guilty and is cooperating with prosecutors.
The case came two years after The Wall Street Journal and The New York Times published reports about the investigation citing anonymous sources.
Prosecutors said from 2008 to 2014, Walters earned profits of $32 million and avoided losses of $11 million trading on inside information about Dean Foods from Davis, and another $1 million trading on a tip about Darden Restaurants.
The U.S. Securities and Exchange Commission in a related lawsuit said Mickelson, who has won three Masters pro golf titles, at one point bought Dean Foods' stock on a recommendation by Walters, to whom he owed money after placing bets with him.
Mickelson was not accused of wrongdoing, but he reached an agreement with the SEC to pay back $1.03 million the regulator said he earned trading shares of Dean Foods.
Lawyers for Mickelson and Davis did not respond to requests for comment.
The case is U.S. v. Davis et al, U.S. District Court, Southern District of New York, No. 16-cr-338.