Tesla's board of directors is gearing up to consider Elon Musk's plan to take the electric carmaker private. But yesterday afternoon—more than two days after Musk's original tweet announcing the proposal—Tesla's board still hadn't been told who would pay for the deal, Reuters has reported.

The board "has not yet received specific information on who will provide the funding," a source told Reuters.

It's the latest sign of how deeply unconventional Musk's take-private plan is.

Ordinarily, a CEO planning a deal of this size would make sure he had all of the details sorted out before making a public announcement. He would get firm commitments from funders. He would get buy-in from the board of directors. And then he'd announce the full details of the plan in a single, thoroughly vetted press release—ideally after markets had closed for the day.

Instead, Musk seems to be making things up as he goes along. We still don't know how the deal would be structured or who would fund it. Tesla board members have said Musk had discussed the possibility of going private with them a week before the public announcement. But talking about it as a theoretical option is very different from being briefed on a specific plan.

Musk has said he wants to allow thousands of small investors to keep their money in the company—despite the fact that SEC regulations are designed to prevent privately held companies from having thousands of shareholders.

Tesla's stock price over the last few days signals growing market skepticism that a take-private deal will actually go through. If the market were confident the deal would go through, the stock should have shot up to nearly the $420 price Musk mentioned in his tweet.

Tesla's stock did soar by 11 percent on Tuesday, to almost $380. But that's a lot less than $420. And since then, Tesla's stock price has declined three days in a row. It's currently around $350—barely higher than the $344 opening price on Tuesday, the day Musk first tweeted about the proposal. That suggests that a lot of traders do not believe that Musk's plan will actually go through.

In any event, Tesla's board now needs to decide whether to approve Musk's plan or not. "The Tesla board of directors plans to meet with financial advisors next week to formalize a process to explore Elon Musk's take-private proposal," sources told CNBC.

Musk will reportedly be asked to recuse himself from the process. A small committee of independent board members will likely take an in-depth look at the proposal and make a recommendation to the full board.

Independent review is important because dissenting shareholders would almost certainly go to court to challenge the deal. To defeat such a lawsuit, it would be very helpful if Tesla could argue that Tesla's independent board members—those without close ties to Musk or Tesla's management—examined the proposal and concluded it was in the interests of all shareholders.

The stakes are particularly high for Musk because federal securities laws make it illegal to manipulate the market using misleading statements. If Musk fails to produce a credible plan to go private—including identifying investors willing to fund the plan—Musk could face lawsuits and SEC scrutiny for tweeting that he had "funding secured" for a deal.