The special committee has the authority to take any action on behalf of the board to evaluate and negotiate a potential transaction and alternatives to any transaction proposed by Musk, the company said in the statement.
He said he had "funding secured" for a deal, but didn't say where the money would come from.
Musk said that since his Twitter post on the possibility of a deal the managing director of the Saudi fund had expressed support for proceeding subject to financial and other due diligence.
"No assurances can be given regarding the likelihood, terms and details of any proposal or potential going private transaction, that any proposal made by Mr. Musk. will be accepted by the special committee", the statement said.
"Despite Elon Musk's frustration with being a public company, I think there are more advantages to remaining public", said CFRA analyst Efraim Levy, citing cheaper access to capital and media exposure due to interest in a public company.
Wall Street had voiced doubts about Musk's ability to pull off what could be the largest-ever go-private transaction, valued at as much as $72 billion.
The first such suit was filed Friday by Tesla short seller Kalman Isaacs, who contended that the tweets were exclusively meant to manipulate the company's stock price - a move that's estimated to have cost Isaacs and those making similar bets upwards of $US1 billion ($1.4 billion).
Musk tweeted on August 7 that he had "funding secured" to buy Tesla shares at $420 per share. Musk allegedly admitted that he "was angry at the company's critics".
Goldman Sachs has always been a key adviser to Tesla, but the apparent involvement of Silver Lake, best known as a private-equity firm specializing in tech investments, is striking. The agency declined to comment.
Musk said on Monday he was in talks with a Saudi sovereign fund for taking the electric auto maker private. But Musk said he was also talking to other investors because he wanted to "continue to have a broad investor base".
He left that meeting on 31 July "with no question that a deal. could be closed - it was just matter of getting the process moving".