The U.S. Justice Department launched the probe after Musk stunned investors in August by tweeting he had "funding secured" to turn the electric-vehicle maker into a private company.
Tesla confirmed that last month it "received a voluntary request for documents from the DOJ and has been cooperative in responding to it."
The company said it has "not received a subpoena, a request for testimony, or any other formal process. We respect the DOJ’s desire to get information about this and believe that the matter should be quickly resolved as they review the information they have received.”
Almost immediately after Musk's unexpected series of tweets suggesting Tesla was poised to go private at $420 per share, market observers began questioning whether the proposal was as solid as Musk suggested.
Soon thereafter, he defended his proposal, saying that Saudi Arabia's sovereign wealth fund had effectively offered to finance the deal.
But later in August, Musk abandoned the bid, saying his financial advisers had decided it wasn't a worthwhile effort and would have unintended consequences. Tesla will stay public.
Bloomberg said the investigation centers on the possibility of "fraud." Federal authorities can crack down on companies or investors who intentionally mislead investors.
Companies convicted of fraud can face sanctions, including major financial penalties, while individuals can face fines, restrictions on their future business activity and prison time.
The criminal probe compounds Tesla's troubles during a crucial period as it seeks to ramp up production of its Model 3 electric car.
But the ripple effects of Musk's dalliance with going private have contributed to increasingly sour sentiment regarding Tesla's prospects.
The company's stock has lost more than a quarter of its value since his initial tweet. And Musk's judgment has come under question after the tweets and a subsequent appearance on a national podcast in which he apparently smoked marijuana.
Tesla shares were down 3.6 percent to $284.20 shortly after noon Tuesday.
The Justice Department and the SEC declined to comment.
Follow USA TODAY reporter Nathan Bomey on Twitter @NathanBomey.