A day after Elon Musk declared that he might try to convert Tesla into a private company, Wall Street banks raced to figure out how such a transaction might work and how they might get a piece of the action.

Executives at banks including Goldman Sachs and Citigroup are discussing ways a deal could be structured, angling to land the potentially prestigious assignment of taking the maker of electric cars off public markets, according to people familiar with the discussions. Bankers and lawyers on Wall Street said any deal is likely to be valued at $10 billion to $20 billion.

Mr. Musk said on Twitter on Tuesday that he had “funding secured” for a deal to take private the electric-car manufacturer that he founded and now leads.

Some senior executives at top Wall Street banks, including JPMorgan Chase and Citigroup, did not hear about Mr. Musk’s idea until his tweet sent Tesla shares soaring shortly after noon on Tuesday, according to people close to the banks. Some bankers grumbled on Wednesday that they had not even been able to get Tesla executives to return their phone calls, much less explain the company’s plans.

Some of Tesla’s big institutional investors — including Fidelity and Saudi Arabia’s Public Investment Fund — also were blindsided by Mr. Musk’s comments, according to people close to those companies.

On Wednesday, officials from the San Francisco office of the Securities and Exchange Commission contacted Tesla officials to inquire about Mr. Musk’s tweets, according to a person briefed on the inquiry. The S.E.C. officials asked Tesla about the veracity of Mr. Musk’s comments and why the company did not make an announcement via a regulatory filing. Tesla shares fell more than 2 percent on Wednesday.

The S.E.C. declined to comment on its inquiry. The Wall Street Journal reported earlier on the inquiry.

A deal to take Tesla private could generate a gusher of fees for Wall Street, and bankers are scrambling to position themselves for an assignment. One way to do that is to come up with possible structures for a deal that they can pitch to Tesla and its advisers.

The traditional way for a publicly traded company to go private is through a leveraged buyout, in which private equity firms or other investors purchase all of the outstanding public shares with money they have borrowed from banks or other sources.

But investment bankers said on Wednesday that a leveraged buyout of Tesla — which in theory could cost as much as $70 billion if all of Tesla’s shares were bought at the price of $420 a share that Mr. Musk floated — is likely a nonstarter. The company, which has never turned a profit, is burning through cash so quickly that it would be hard to find banks or bond investors willing to lend tens of billions of dollars to finance a private buyout.

“The numbers don’t work as it is,” said Ronald A. Kahn, the head of the debt advisory and valuation practice at Chicago-based investment bank Lincoln International. “Why would anyone even give him a few billion more?”

That does not mean, however, that a deal to take Tesla private is off the table.

One structure being studied by banks and Tesla, according to people familiar with the matter, is a transaction that would reduce the number of shareholders to such a degree that Tesla’s shares could be delisted from the Nasdaq stock exchange and the company no longer would be required to make quarterly filings with the S.E.C.

That would be expensive — it could cost $10 billion to $20 billion — but much less so than a full leveraged buyout, these people said.

How might such a transaction work?

One possibility is a maneuver called “going dark.” In this situation, Tesla could buy out many but not all of its shareholders to reduce the total number of investors who hold Tesla stock. One way to make that math work would be to persuade as many small shareholders as possible to sell their holdings.

The largest shareholders of the company — including Mr. Musk, Fidelity, T. Rowe Price and Scotland’s Baillie Gifford, who collectively own about 45 percent of Tesla shares — would not need to sell their stakes under that arrangement.

Tesla’s shares would no longer be listed on the Nasdaq, but investors could buy or sell them on loosely regulated, over-the-counter markets that are typically the domain of small companies. Because shares on these exchanges are generally traded less heavily than those on larger public markets, it would likely be harder for investors to bet against, or short, Tesla’s stock, which is one of the rationales Mr. Musk outlined on Tuesday for taking the company private.

There are many potential problems with this approach. For example, institutional and individual investors are likely to object to holding Tesla shares that do not trade on mainstream national exchanges. In addition, index funds that own Tesla stock could probably not hold the shares if they were not part of benchmarks like the Standard & Poor’s 500-stock index.

Going-dark transactions traditionally have been the province of tiny companies, said Gilbert J. Bradshaw, a New York lawyer who works with small companies and has written about companies going dark.

“I don’t know of any large company that has done a voluntary deal like this,” he said.