"We are cooperating with investigators and take those probes seriously", a Facebook spokesman told the Times in a statement.
Manufacturers of mobile devices got an especially sweet deal, according to internal Facebook documents seen by the Times.
The exact focus of the investigation, however, remains unknown.
Last July, Facebook began facing a widening inquiry from the federal government, with three federal agencies and the Department of Justice looking into how the political-consulting firm Cambridge Analytica obtained the personal data of up to 87 million Americans.
The criminal investigation adds to a laundry list of probes since the Cambridge Analytica revelations one year ago placed a spotlight on the company's data and privacy practices.
Facebook has defended the deals. It reports that both companies had data partnerships with Facebook that gave them access to the personal information of hundreds of millions of users.
The social media giant acknowledged the report in a tweet, saying that it is already facing federal investigations.
Those companies were not named in the story, but the Times noted that Facebook has data-sharing partnerships with companies including Microsoft, Apple, Sony and Amazon.
Facebook did not immediately respond to a request for comment. Numerous partnerships ended years ago, the Times noted, but the deals with Amazon and Apple were ongoing at the time of the story. There have also been reports that the company is negotiating a multi-billion dollar fine with the Federal Trade Commission over the company's privacy failures.