Being a public company means being subjected to wild swings in stock prices (it even spiked earlier today after his tweet talking about taking the company private), and such volatility can be a "major distraction" for both Tesla's workforce and shareholders.
While no final decision has been made, he suggested a buyout price of $420 per share.
Tesla has had more than its share of ups and downs over the past few months, due to an intense focus on production rates and sales figures for Tesla's mass-market Model 3 electric auto. At $420 a share, Tesla would have a market cap of around $71 billion.
In a second tweet on Tuesday, Mr Musk said taking the company private would not lead to a single dominant shareholder.
Tesla and its investors are no stranger to seeing the company's share price follow a rollercoaster trajectory.
In its second quarter results for 2018 the company posted $4bn of revenue and a loss of $717m. The company had a market value of $58 billion as of Monday's close. At the time, Tesla shares were trading at about $360 per share and went as high as $371.15 before giving back gains later in the afternoon. "Funding secured", Mr Musk wrote in his first tweet, following up with "good morning" and a smiley emoji. Musk said he is considering taking the electric auto maker private.
And yet it also left many questions unanswered, namely how Musk - who owns nearly 20 percent of the company - would be able to come up with the $66 billion necessary to complete the transaction. Shares jumped in Tuesday trading following reports that the Saudi Arabian sovereign wealth fund took a $2 billion stake in the company earlier this year.
During a conference call in May, Mr. Musk shut down questions from analysts, calling them "boring" and spent much of the time talking to an investor who runs a YouTube channel, prompting an after-market sell-off of Tesla's shares.
While Mr Musk has previously discussed the drawbacks of being a public company, he has also used his Twitter account in ways that surprised investors.
Scottish money manager Baillie Gifford, which recently urged Musk to focus less on tweeting and more on running the business, is the fourth-largest shareholder, with a almost 8% stake. This would enable you to still share in the growing value of the company that you have all worked so hard to build over time.
"This has nothing to do with accumulating control for myself", he said.