An investor,

Glen Littleton,

sued Tesla, Mr. Musk and members of Tesla’s board at the time, alleging that Mr. Musk’s tweets were false and cost investors billions by spurring swings in the prices for Tesla stock, options and bonds. In court filings, Mr. Musk has said he was indeed considering taking Tesla private and believed he had the support of Saudi Arabia’s sovereign-wealth fund to do so. The deal, which would have been valued around $72 billion, never materialized.

U.S. District Judge

Edward Chen,

who is overseeing the San Francisco jury trial that is scheduled to run through Feb. 1, has ruled that Mr. Musk’s tweets about taking the company private weren’t true and that he acted recklessly in making them. 

Questions for the jury include whether Mr. Musk’s tweets were material to investors and whether he knew they were untrue.

The case is unusual in that securities-fraud cases usually resolve before going to trial, such as through a settlement, said

Jill Fisch,

a securities-law professor at the University of Pennsylvania. The defendants in this case face “an uphill battle” in light of the judge’s pretrial decision about the veracity of Mr. Musk’s statements, she said.

Attorneys for the lead plaintiff didn’t respond to a request for comment, nor did an attorney for Tesla, Mr. Musk and the other board members.

Mr. Musk is expected to take the stand as early as Wednesday, some two months after he did so in Delaware in a trial over his pay package at Tesla. In 2021, he also appeared before Delaware’s business-law court to defend Tesla’s roughly $2.1 billion 2016 takeover of home-solar company SolarCity Corp. 

Also on the list of possible witnesses are Tesla board chair

Robyn Denholm,

board members

Ira Ehrenpreis,

James Murdoch

and

Kimbal Musk

—the CEO’s brother. The head of investor relations,

Martin Viecha,

also may be called.

This week’s trial comes at a busy time for Mr. Musk, who has been scrambling to turn around Twitter Inc. after buying the social-media company last fall in a deal valued at $44 billion. His rocket company SpaceX is pushing for the first orbital launch of a new rocket Mr. Musk wants to use for deep-space missions. 

Tesla, meanwhile, has slashed prices across its vehicle lineup, with some of last week’s cuts in the U.S. nearing 20%, in a bid to juice demand. The company’s stock has fallen roughly 70% since its peak in November 2021, erasing around $850 billion in market value. Mr. Musk’s personal wealth has fallen more than $200 billion in that time, according to the Bloomberg Billionaires Index.

Court proceedings involving Mr. Musk can be feisty. In the SolarCity case, for example, Mr. Musk called opposing counsel a “bad human being.”

In advance of this week’s trial, Mr. Musk asked the court to move the trial to Texas on the basis that potential jurors in San Francisco could be biased against him. Judge Chen rejected the request. 

“It isn’t that hard it seems to me to find 15 people,” he said.  

The court requires nine jurors and six alternates to proceed with the case. Roughly 190 potential jurors were asked to fill out questionnaires about their views of Mr. Musk and other issues. The court plans to bring in about 50 of them for further questioning Tuesday. 

Opening arguments could start as early as Tuesday after the jury is selected.

The lead plaintiff is seeking damages for investor losses he alleges stemmed from Mr. Musk’s and Tesla’s statements. Tesla stock closed up 11% the day Mr. Musk initially tweeted about potentially taking Tesla private, later giving back all those gains and falling further as questions emerged about the deal. 

The defendants have said the plaintiff won’t be able to prove to a jury that the statements were materially false. Mr. Musk was considering taking Tesla private, the defendants have said, even if some of his assertions about the deal may not have been literally accurate.

Defendants, in a trial brief, said Mr. Musk believed he had secured backing to take the car maker private from Saudi Arabia’s sovereign-wealth fund, the Public Investment Fund. A lawyer for the defendants said Friday that his team had chosen not to enforce subpoenas calling on fund representatives to testify. The sovereign-wealth fund didn’t respond to a request for comment.

Mr. Musk and Tesla each agreed in 2018 to pay $20 million to settle civil charges brought by the Securities and Exchange Commission over the same tweets. Mr. Musk also agreed to step down as chairman of the company, while remaining CEO. He later said in legal filings that he felt pressured to settle with the SEC. Last year, a federal judge denied Mr. Musk’s request to scrap his settlement.

Write to Rebecca Elliott at rebecca.elliott@wsj.com and Meghan Bobrowsky at meghan.bobrowsky@wsj.com