Mr Musk said in his tweet on Tuesday that shareholders would be offered $420 (£326) per share, valuing the business at more than $70bn.
Tesla's shares were down less than one per cent at $376.31 USA in morning trading on Wednesday after closing up 11 per cent at $379.57 United States on Tuesday.
Tesla Inc said on Wednesday its board is evaluating chief executive Elon Musk's idea of taking the company private after he brought the matter up for discussion last week.
Tesla's stock has swung wildly in the past several years, hit by the company's production issues as well as Musk's own explosive remarks on Twitter that have turned off investors.
Some Wall Street analysts are skeptical of Musk's ability to gather the financial backing to complete such a deal.
"Who gives $30 to $50 billion to buy back the shares?" asked NordLB analyst Frank Schwope. The company already has a $2 billion investment from Saudi Arabia's sovereign fund as well as Tencent, which took a 5 percent stake in 2017.
China's Tencent Holdings Ltd, which took a 5-percent stake in Tesla previous year, could also be a possible partner.
Musk later tweeted that existing stockholders could choose whether to hold onto their shares or sell them to the new investors for $420 a share.
He said that would allow Tesla to "operate at its best, free from as much distraction and short-term thinking as possible".
Some on Wall Street shared that view.
Tesla Inc Chief Executive Officer Elon Musk'splan to take the electric auto maker private raised doubts among Wall Street analysts about the billionaire' s ability to gather enough financial backing to complete the deal.
Musk hasn't been quiet about his disdain for short sellers.
Six members of Tesla's board of directors issued a statement Wednesday, acknowledging that discussions have been ongoing since last week about going private. Rather, it was attributed to Brad Buss, Robyn Denholm, Ira Ehrenpreis, Antonio Gracias, Linda Johnson Rice, and James Murdoch. They did not include Mr Musk, his brother Kimbal Musk, and Steve Jurvetson, a venture capitalist.
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