In the past year, the stock has traded as low as $244.59 in April and as high as $389.61 in September.
The electric car maker went public in 2010. Its current market value is $61 billion. At a share price of $420, the company would be worth $71.3 billion.
Although Musk mentioned funding in his initial tweet, a blog post from Tesla did not include any mention of financing. CNBC also contacted a number of Wall Street banks and none of them was aware of any transaction or had committed to funding a leveraged buyout of Tesla.
The Securities and Exchange Commission also declined to comment on the matter. However, companies are allowed to use social media outlets like Facebook and Twitter to announce news, the SEC said in 2013.
Musk also said he does not currently have a controlling vote in the company and wouldn't expect a single shareholder to have one if the company were private. He said he had no intention of selling his stake, and he said he would remain as CEO.
Taking Tesla private could remove some of the pressure on the closely watched company. Private firms, for example, are not required to publicly report quarterly earnings. Musk also said being private would end "negative propaganda from shorts."
The CEO has said he expects Tesla to begin being profitable in the third quarter of 2018.
Investors have been concerned about the amount of cash Tesla has been burning through and whether the company would need to raise additional funds to support its growth plans, which include introducing a semi-truck, a crossover SUV called the Model Y, more factories around the world, and other projects.