Tesla Inc. Chief Executive Officer Elon Musk's plan to take the electric car maker private raised doubts among Wall Street analysts about the billionaire's ability to gather enough financial backing to complete the deal.

Musk shocked the market, yet again with a tweet on Tuesday that he was considering taking the loss-making company private at $420 a share. Shares were down 3 percent in premarket trading after closing up 11 percent at $379.57 on Tuesday.

"Given the haphazard process of disclosure last afternoon, our initial impression was that Elon Musk sprung his plan of going private upon the public without consulting Tesla's board of directors or major shareholders," Bernstein analysts said in a note titled "Going private? Who knows... does Elon?"

Most analysts were skeptical, but some said a deal could materialize if Musk succeeded in lining up the right funding. 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.

"Elon's tone and messaging regarding a potential transaction lead us to believe that there could be significant outside funding lined up," RBC analysts said.

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.

The move to take the company public would remove Musk, who himself has a 20 percent stake, from the public arena -- and contentious criticism.

"Distraction or not, the move feels right even if Musk is downplaying how supportive public markets have been. With Tesla unable to take on more debt, we wonder who may fund the potential deal and end up as a new large shareholder," Jefferies said in a note.