If the transaction got done at $420 per share, Tesla would be valued at just over $70 billion, making it the biggest deal in which a company is taken private.

Although Tesla has become the most valuable American car company, it has yet to turn an annual profit since its founding in 2003. And its chief executive, a 47-year-old native of South Africa, has come under increasing pressure as he has scrambled to increase production of the Model 3, a midsize sedan that he is counting on to drive up revenue and enable the company to become profitable.

Still, this is not the way multibillion-dollar leveraged buyouts are typically announced. Companies would normally line up banks, private equity firms or other deep-pocketed investors to agree in advance to provide money to finance the purchase of shares.

Officials representing a number of large banks and investment funds said on Tuesday that they had not talked with Tesla about financing a buyout, although it is possible the company had secured funding from other sources.

Mr. Musk’s comments on Tuesday — mentioning the specific price of a possible buyout and declaring that Tesla had already arranged funding — were virtually guaranteed to send the shares flying. Still, while it was unusual for a chief executive to make a market-moving announcement on Twitter, there is nothing improper about it on its face.

In 2013, the Securities and Exchange Commission said it was permissible for companies, and people acting on their behalf, to make announcements using social media platforms like Twitter and Facebook. It said companies had to alert investors in advance that those would be channels for important corporate news. And Tesla did so, in a filing in 2013.

But the S.E.C. has also advised that intentional releases of market-moving information on social media platforms or websites must be accompanied by a simultaneous release to the broader public. The delay between Mr. Musk’s tweet and Tesla’s corporate announcement could be of interest to the S.E.C., said Michael Liftik, a former deputy chief of staff at the commission who is now a partner at the law firm Quinn Emanuel Urquhart & Sullivan.