The Securities and Exchange Commission (SEC) has inquired with Tesla about CEO Elon Musk's tweets regarding his plans to take the company private, The Wall Street Journal reported Wednesday.

Trading on the company's stock was halted Tuesday after Musk tweeted that he was considering taking Tesla private.

The Journal reported that the securities regulator is looking into the legitimacy of Musk's comments, and why he made the disclosure on Twitter instead of through a formal filing.

"Am considering taking Tesla private at $420. Funding secured," Musk tweeted Tuesday afternoon, initially offering little context.

The message set off a scramble among reporters and shareholders.

"Shareholders could either to sell at 420 or hold shares & go private," he later added.

Musk later elaborated in a letter to Tesla employees saying that he was exploring the option.

He explained that, ideally, he would restructure the company in a similar manner to his other company, SpaceX, giving employees shares of the company and allowing them to buy or sell them periodically.

Former SEC Chairman Harvey Pitt told CNBC on Wednesday that Musk could face criminal and civil penalties if investigators find he did not secure funding prior to the time of his tweet.

An SEC investigation would be the latest among a string of recent hiccups for Musk and Tesla.

The company posted its biggest loss in its history in the second quarter of 2018, booking a net loss of $717.5 million. The company still had $2.78 billion in cash, and vowed to turn profits during the remainder of the year.

Musk, earlier this year, landed in hot water when he called a British diving expert a "pedo" after he dismissed Musk's efforts to assist in the rescue a group of Thai children in a cave as a "PR stunt." Musk later apologized for his remarks.