Investigators are focusing on calls and contacts White, a former vice chairman at the collapsed energy trader, made in October, when he sold half his holdings, or $3.08 million in Enron stock, the paper reported.
FBI agents have been interviewing White's friends and former colleagues about whether he sought or acted on inside information from them on the company's fast deteriorating finances last call, the paper reported.
But several interviewed by the FBI say they've told the agents that the calls were largely personal and didn't involve insider information, the Journal reported.
White is already being investigated by the Defense Department's inspector general for his travels, having raised eyebrows with a recent trip to Aspen, Colorado, aboard an Army aircraft to sell a house.
White has in the past denied knowledge of Enron's off-balance sheet partnerships that allowed it to keep large amounts of debt off its books and maintain investment grade debt rating.