Investors must file a public form when they purchase more than 5% of a company's shares. By delaying the report to April 4, at least 10 days past the deadline, Musk was able to purchase more Twitter stock without other shareholders being alerted to his purchase.
The disclosure can be a sign to shareholders and corporations that an investor may be attempting to influence or control a company.
If the stock market knew of the Tesla CEO's growing stake in Twitter, the share price could have risen.
Musk's delay may have saved him more than $143 million, University of Pennsylvania accounting professor Daniel Taylor told WSJ.
If the report is true, this would not be the first time the Securities and Exchange Commission has gone after Musk.
A judge ruled last month that Musk must comply with a multi-million-dollar securities fraud settlement with the SEC after he tweeted threatening to take Tesla private in 2018, The Associated Press reported.