Mr Musk said de-listing from the stock exchange meant Tesla would no longer be pressured into making short-term decisions to appease investors.
In an unusual move, Mr Musk first made the announcement on Twitter rather than via an official regulatory disclosure.
But analysts and bankers are sceptical he could push through such a huge deal.
Mr Musk said shareholders would be offered $420 per share – around a fifth higher than the current price. That values the business at more than $70bn.
Tesla boss Elon Musk is considering taking the electric-car firm private, a move he claimed was the “best path forward” for the company
He claimed to have secured funding to buy out shareholders, but did not provide details.
However, he also warned that “a final decision has not been made” about the move. Any buy-out would need a shareholder vote.
Mr Musk, who owns almost 20% of the company, said he hoped the move would shield the firm from distracting swings in the share price and the pressure to meet quarterly financial targets.
He also said he wanted to end “negative propaganda” from short sellers, investors who bet on the shares of a firm going down.
“Basically, 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,” he wrote.
Mr Musk has discussed the drawbacks of being a public company before. But his tweets stirred confusion initially, given his history of informal use of the social media service.
For example, on April Fool’s Day, he joked on Twitter about Tesla going bankrupt.
If Tesla were taken private at $420 per share, it would be one of the largest such transactions in history.