Members of the Tesla board said Wednesday that they have met "several times" to discuss CEO Elon Musk's desire to go private.

Musk tweeted Tuesday that he was "considering taking Tesla private" and that he had the funding in line to do so — sending shares up in a busy day of trading and spurring confusion around Wall Street. The company elaborated on the tweet later Tuesday, saying "a final decision has not yet been made."

Musk raised the discussion with the board last week, the statement says, lending some legitimacy and context to Musk's original tweet. Musk has several reasons to favor taking Tesla private, but would need billions of dollars and board support to do it at his proposed price of $420 per share.

The statement Wednesday was not made on behalf of the full board. It was signed by board members Brad Buss, Robyn Denholm, Ira Ehrenpreis, Antonio Gracias, Linda Johnson Rice and James Murdoch. Tech VC Steve Jurvetson remains on leave from the board and Kimbal Musk, Elon's brother, recused himself, Tesla said in a statement to CNBC.

Here's the full statement:

Last week, Elon opened a discussion with the board about taking the company private. This included discussion as to how being private could better serve Tesla's long-term interests, and also addressed the funding for this to occur. The board has met several times over the last week and is taking the appropriate next steps to evaluate this.

—CNBC's Meghan Reeder contributed to this report.