Individuals identified only as people familiar with the case said Bachus is being investigated by the Office of Congressional Ethics, an independent investigative agency, the newspaper reported.
Roll Call Friday reported the Bachus case likely is one of four opened by the office in the fourth quarter of 2011, with five other cases in a second-phase review.
Bachus, chairman of the House Financial Services Committee, has frequently bought and sold stock options while overseeing the nation's banking and financial services industries, the Post said.
The ethics office's investigators have told Bachus he is under investigation and that there is probable cause to believe insider-trading violations occurred, the Post said.
Word of the investigation came as the House passed legislation Thursday to tighten rules against insider trading by lawmakers. The Senate passed its version last week.
"The Office of Congressional Ethics has requested information and I welcome this opportunity to present the facts and set the record straight," Bachus said in a statement issued through his spokesman, Tim Johnson.
The Post said attorneys for the office and the House Ethics Committee declined comment.
Roll Call said the ethics office has 45 days to complete its investigation, which can then be extended for 45 days.
Rep. Barney Frank, D-Mass., the ranking Democrat on the House Financial Services Committee, told Roll Call he has always found Bachus to be "honorable and straightforward" even though the two disagree on policy issues. He refused to comment directly on the reported investigation.
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