The directors Brad Buss, Robyn Denholm, Ira Ehrenpreis, Antonio Gracias, Linda Johnson Rice and James Murdoch said: "Last week, Elon opened a discussion with the board about taking the company private".
In the last week, Tesla's board has met "several times" to discuss Musk's proposal and "is taking the appropriate next steps to evaluate this". 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.
Several securities attorneys told Reuters that Musk could face investor lawsuits if it was proven he did not have secure financing at the time of his tweet.
Shares rocketed up 11 percent after Musk's grand reveal Tuesday, with some expecting they would hit $420 - the price Musk had promised shareholders would receive once the company had finalized its go-private transformation.
Tesla's shares were down less than one per cent at $376.31 United States in morning trading on Wednesday after closing up 11 per cent at $379.57 USA on Tuesday.
"Who gives $30 to $50 billion to buy back the shares?", asked NordLB analyst Frank Schwope.
It's possible Musk could persuade some large institutional investors to remain shareholders in the private company, which could reduce his funding needs, Sacconaghi said.
In that time, Tesla short-sellers - Musk's sworn enemies - may have lost more than $800m, according to estimates from financial-technology firm S3 Partners, while his 20% stake reportedly gained $851m.
"What does Musk mean by 'funding secured?"' asked Toni Sacconaghi, an analyst at Bernstein who has always been bearish on Tesla shares.
Two of the potential stumbling blocks to Musk's plan include the stock price premium not being enough to get the existing shareholders on board to support the sale and coming up short on the announced funding to complete the transition.
"This proposal to go private would ultimately be finalized through a vote of our shareholders", Musk said in explaining the potential move.
A statement was issued by six members of the electric carmaker's board after Mr Musk tweeted to say he had the funding to de-list the company. That last part is important, because Tesla's going to need a lot of it.
Names excluded from the board statement were Musk; his brother, Kimbal Musk; and Steve Jurvetson, a venture capitalist and early Tesla backer who's been on leave since previous year.