• The SEC is investigating whether recent stock sales by Tesla CEO Elon Musk and his brother Kimbal Musk violated insider trading rules, the Wall Street Journal reported Thursday.
• The probe reportedly focuses on stock sales by Kimbal Musk that occurred one day before Elon Musk asked his tens of millions of followers on Twitter to vote in an informal poll, asking whether he should unload some of his Tesla shares.

The Securities and Exchange Commission is investigating whether recent stock sales by Tesla CEO Elon Musk and his brother Kimbal Musk, who sits on Tesla's board of directors, violated insider trading rules, the Wall Street Journal reported Thursday, citing people familiar with the matter.

Shares of Tesla dipped momentarily on the news but recovered and were up more than 4% in afternoon trading.

The SEC probe reportedly began last year and focuses on stock sales by Kimbal Musk that occurred one day before Elon Musk asked his tens of millions of followers on Twitter to vote in an informal poll, telling them their vote would determine the future of his Tesla holdings.

The SEC declined to comment on the report. Musk did not respond to a request for comment.

However, in an email exchange with CNBC on Tuesday, Musk did mention an upcoming story about Tesla and the SEC that the Journal was apparently working on.

When CNBC asked about his lawyer accusing the SEC of leaking information, Musk wrote: "The SEC leaked confidential information to the WSJ, deliberately violating federal law. We found out about this because, in their eagerness to gain a scoop, WSJ jumped the gun and inquired about it with Tesla before, rather than after, SEC publication."

CNBC reached out to the SEC and Wall Street Journal for comment on Elon Musk's leak allegation. The SEC did not respond. The Journal declined to comment on its sourcing for the story.

Musk also opened up to CNBC about his tense relationship with President Joe Biden and cheered on the Justice Department probe of short sellers.

Musk wrote to his 62.5 million Twitter followers on November 6, 2021: "Much is made lately of unrealized gains being a means of tax avoidance, so I propose selling 10% of my Tesla stock. Do you support this?" Some 3,519,252 people responded, and 57.9% of them voted "Yes" according to the count displayed by Twitter.

Kimbal Musk sold around $109 million worth of his shares the day before his CEO brother's Twitter poll, according to financial filings.

Shares dropped on the Monday after Elon Musk's Twitter poll a few days earlier.

They had been climbing since late October 2021, following a strong 2021 third quarter, and an announcement from rental car company Hertz that it was ordering 100,000 Tesla vehicles for its fleet.

Elon Musk waited for a week after Hertz made its announcement to clarify that Tesla hadn't signed a contract with the rental car company yet. Before the clarification, he taunted investors who were short shares of Tesla on Twitter, writing: "Tesla Hertz shorts."

While some fans believed they were advising Musk on his stock sales by voting in his Twitter poll, the Tesla CEO said in Sept. 2021 he was likely to sell "a huge block" of his options in the fourth quarter at an appearance at the Code Conference.

He also said he had to sell a large portion of his shares to cover his tax bill.

Most of the insider transactions by the Tesla chief and centibillionaire were part of a "Rule 10b5-1" trading plan dated Sept. 14, 2021, according to public filings. This type of plan allows company insiders to execute trades in their own company's stock for a set, future date.

Musk has been locked in a battle with the SEC after they charged him with civil securities fraud in 2018. Tesla, Musk and the SEC struck a revised settlement agreement in 2019 to resolve the charges.

As part of the deal, Musk had to relinquish his role as chairman of Tesla's board for 3 years, and the CEO could not claim innocence after the settlement, but the settlement was not a determination of guilt.

Musk most recently accused the SEC of "unrelenting investigation" amounting to harassment, and of retaliating against him for his public criticism of the federal financial regulators.

-- CNBC's Brian Schwartz contributed reporting.

Read the full story from the Wall Street Journal here.