Unidentified sources told Bloomberg News that prosecutors in the Manhattan U.S. Attorney's Office "were provided with information about key exchanges concerning Bezos."
The news outlet reported the investigation was centered on determining whether the company violated a stipulation that AMI not engage in criminal conduct.
The company was granted immunity as part of a probe into hush-money payments made to former Playboy Playmate Karen McDougal and adult film star Stormy Daniels, according to The Wall Street Journal.
Update 10:35 a.m. EST Feb. 8: The National Enquirer's parent company, American Media LLC, defended the tabloid's actions Friday in a statement.
“American Media believes fervently that it acted lawfully in the reporting of the story of Mr. Bezos,” the statement said.
Company officials said American Media’s board has voted to investigate the situation.
“Upon completion of that investigation, the board will take whatever appropriate action is necessary,” the statement said.
The Enquirer published a story last month that included lurid texts between Bezos and former TV anchor Lauren Sanchez. Since then, private investigators have been looking into how the Enquirer got the texts.
Bezos says he was the target of "extortion and blackmail" by American Media. But the company says it engaged in "good faith negotiations."
Original report: Bezos said the tabloid's parent company, AMI, somehow acquired private text messages and photos of him and his girlfriend, Lauren Sanchez, and threatened to release them publicly if he didn't stop his investigation into how they were leaked.
Bezos said the tabloid did publish private text messages a few weeks ago, which prompted him to hire a private investigator.
“Of course I don’t want personal photos published, but I also won’t participate in their well-known practice of blackmail, political favors, political attacks and corruption,” Bezos said in his letter.
He also explained why he decided to go public with the “extortion” attempt.
“I prefer to stand up, roll this log over and see what crawls out,” he said.
Bezos included a letter and other communications from AMI’s lawyer.
Bezos' private investigator, Gavin de Becker, said in recent interviews that he was looking into whether Sanchez's brother, a supporter of President Donald Trump, may be responsible for the leaks, according to The New York Times.
Trump has repeatedly bashed Bezos and Amazon on social media since becoming president.
The Associated Press contributed to this report.