Tesla declined to comment. The SEC did not immediately respond to a request for comment.

The agency is pressing Tesla's board for details on how much information he shared with them prior to announcing his plans on Twitter, the report said, citing a source. Two key questions are what Musk may have told directors before he spoke publicly about the possibility of taking Tesla private and when he spoke to them.

The Securities and Exchange Commission is looking into whether Tesla CEO Elon Musk tweeted about taking the company private in order to hurt those who were shorting Tesla's stock, according to a report in the Wall Street Journal Thursday.

Last week, short-sellers betting against Tesla lost big after the CEO tweeted "considering taking Tesla private at $420 a share. Funding secured." At that level, the company would be valued at $72 billion.

"Funding Secured"

Tesla shares rose 11 percent following Musk's tweet on Aug. 7, meaning short sellers lost about $1.3 billion in mark-to-market losses, according to estimates from financial technology and analytics firm S3 Partners.

The data firm said roughly 35 million Tesla shares are held short and the cumulative mark-to-market paper loss for those betting against the automaker as of last week was roughly $3 billion for this year. Short selling is a practice in which traders can bet against a company by selling shares they don't own and buying them back at a lower price.

There are few if any details on where the money for a deal like this would come from. Some legal experts have said that if Musk really had not secured the funding for the deal, he could be accused of fraud or market manipulation.

Since his first tweet Musk said in a blog post that he had had conversations with members of the Saudi Arabian wealth fund about investing in a buyout deal, and said he is working with Silver Lake Partners and Goldman Sachs on the deal. Goldman Sachs moved Tesla to "not rated" status on Wednesday and confirmed it is advising Musk on the deal.

Tesla shares closed Thursday at $335.45, down less than 1 percent, and valuing the company at $57.2 billion.