WASHINGTON—U.S. regulators are asking Tesla Inc. whether Chief Executive Elon Musk was truthful when he tweeted that he had secured funding for what would be the largest-ever corporate buyout, people familiar with the matter said.

Officials at the Securities and Exchange Commission want to know whether Mr. Musk had a factual basis for tweeting Tuesday that the going-private transaction was all but certain, with only a shareholder vote needed to pull it off, the people said.

The SEC’s inquiries, which originated from the agency’s San Francisco office, suggest Tesla could come under an enforcement investigation if regulators suspect that Mr. Musk’s statement was misleading or false.

It couldn’t be learned on Wednesday whether the agency had opened a formal enforcement investigation. An SEC spokesman declined to comment. Tesla didn’t respond to a request for comment.

Under U.S. law, companies and corporate officers can’t give shareholders misleading information about meaningful company events. Mr. Musk also could be in trouble if regulators develop evidence that he made a statement aimed at goosing his company’s share price.