Shares rose 11 percent Tuesday but fell almost 2 percent at midday Wednesday to $372.38.
Musk later clarified in a blog post that "a final decision has not yet been made", while touting the benefits of running a private company away from the "enormous pressure" of Wall Street's quarterly earnings cycle.
Elon Musk is serious enough in his publicly-stated interest about taking Tesla private that the board of directors has already discussed the matter several times.
The board members said they were "taking the appropriate next steps" to evaluate the proposal. Musk's money-losing and cash-burning company is an unlikely candidate for debt investors to be willing to help go private.
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 U.S. on Tuesday.
Musk owns an nearly 20 per cent stake in Tesla, meaning he'd still need roughly $70 billion in financing to take Tesla private.
"I'm trying to accomplish an outcome where Tesla can operate at its best, free from as much distraction and short-term thinking as possible, and where there is as little change for all of our investors, including all of our employees, as possible".
FILE PHOTO: Elon Musk, founder, CEO and lead designer at SpaceX and co-founder of Tesla, speaks at the International Space Station Research and Development Conference in Washington, U.S., July 19, 2017.
Musk has promised a sustained net profit starting in the third quarter.
SoftBank is now not interested in a deal for Tesla after earlier this year taking a stake in General Motors Co's (GM.N) self-driving unit, Cruise, Reuters reported earlier on Wednesday.
"What does Musk mean by 'funding secured?"' asked Toni Sacconaghi, an analyst at Bernstein who has always been bearish on Tesla shares.
China's Tencent Holdings Ltd, which took a 5-percent stake in Tesla past year, could also be a possible partner.
"Just because" Musk wants it at $420 "doesn't mean that there aren't other people who might be willing to come in with another transaction that would be more beneficial to shareholders", Pitt said.
Among these issues, short-sellers have especially posed a continuous problem for Tesla, and it's no surprise Musk would like to put an end to the roller coaster that their actions can cause, with him highlighting the view that Tesla is one of most shorted companies on Wall Street.