The Wall Street Journal reported that the Securities and Exchange Commission launched a probe into Musk after he delayed reporting his large stake in the company, a move that could have saved him millions of dollars.
The SEC investigation has not been made public by regulators, but the Journal said it was based on people familiar with the matter.
Musk missed the SEC's 10-day disclosure deadline by more than a week because he didn't report his 5% stake in Twitter until April 4.
After reaching 5% ownership, Musk continued to buy Twitter stock at relatively low prices before publicly revealing his 9.2% stake in the company in an SEC filing.
Daniel Taylor, an accounting professor at the University of Pennsylvania, told the Journal that the SEC could bring civil charges against Musk.
Musk was sued last month by a shareholder who alleged that he cheated shareholders when he filed a disclosure form with the SEC.
The company's board accepted Musk's offer to buy the entire company for $44 billion.
A representative for Musk did not respond to a request for comment when the SEC declined to comment on the reported probe.
The shareholder sued Musk, saying he misled investors.