After Musk last week raised the idea as a better solution for Tesla's long-term growth, directors met "several times" and are "taking the appropriate next steps to evaluate this," the board said in a brief statement issued before the stock market opened.
Musk jolted markets Tuesday by announcing the proposal on Twitter and saying he could finance the buyout at a large premium to current valuation, at a price of $420 (roughly Rs. 28,800) a share.
Going private would liberate the company from the quarterly reporting cycle, making it "free from as much distraction and short-term thinking as possible," Musk said in a blog post.
Musk, who has stirred controversy with his unorthodox management style and often confrontational approach to critics, said he viewed going private as "the best path forward," but a final decision had not been made and ultimately rested on shareholder support.
Shares of Tesla were down 2.1 percent $371.60 (roughly Rs. 25,500) in early trading Wednesday.
Trading in the company was suspended Tuesday for about 90 minutes after Musk's surprise announcement. Shares finished the session 11 percent higher.
Many companies avoid releasing market-moving news during trading hours, but Musk floated the idea in an afternoon tweet and then elaborated in a series of responses to questions on the social network, before finally releasing a letter to employees with more details on the rationale.
He said current shareholders would be protected and allowed to continue to participate in the company's growth.