Elon Musk is seeking to have a coming securities-fraud trial involving his conduct running Tesla Inc. moved out of San Francisco, arguing that negative publicity surrounding his use and recent management of Twitter has biased local jurors against him.

San Francisco’s jury pool has been “exposed to excessive and adverse pretrial publicity concerning Defendant Elon Musk that will deprive him of an impartial jury and his constitutional right to a fair trial,” Mr. Musk’s attorneys argued in a Friday court filing.

Mr. Musk and Tesla are facing a trial scheduled to begin this month over a shareholder lawsuit relating to his tweets in 2018 suggesting he had funding to take the electric-vehicle company private.

Mr. Musk purchased San Francisco-based social-media site Twitter Inc. in late October and soon after laid off about half of its staff. Mr. Musk’s attorneys argued in a court filing that Twitter’s recent staff reductions, including almost 1,000 employees in the federal-court district that includes San Francisco, have caused prejudice against Mr. Musk among jurors “who were personally impacted or are close to those personally impacted.” Mr. Musk’s lawyers also cited negative responses from local politicians and media in the filing.

Mr. Musk tweeted in 2018, “Am considering taking Tesla private at $420. Funding secured.” The deal that would have been valued at $72 billion at the time never materialized. Investors sued Tesla and Mr. Musk, claiming his tweets were false and cost them billions by spurring swings in Tesla’s stock price. In court filings, Mr. Musk has maintained that his tweets were accurate and that Saudi Arabia’s sovereign-wealth fund had agreed to support his attempt to take Tesla private. U.S. District Judge Edward Chen, who is overseeing the case, last year ruled that Mr. Musk’s tweets about taking the company private were false and misleading. 

Mr. Musk and Tesla each paid $20 million to settle a civil lawsuit by the Securities and Exchange Commission over the tweets in 2018. Mr. Musk also relinquished the role of Tesla chairman, though he remained as the company’s chief executive. He later said in legal filings that he felt pressured to settle the suit. Last year, a federal judge denied Mr. Musk’s request to scrap the settlement. 

Mr. Musk’s attorneys also wrote in the filing that the local press has accused Mr. Musk of “encouraging and personally participating in the purported spread of misinformation” on Twitter. His attorneys argued that this coverage might make potential San Francisco jurors “unable to impartially evaluate” Mr. Musk’s conduct in connection with the 2018 tweets that are at issue in the trial.

The motion proposes that the trial be held in western Texas. Tesla moved its headquarters from northern California to Austin in late 2021. Tesla has 47,000 employees in California, according to a Tesla blog post published this week.

Should the trial’s venue not be moved, Mr. Musk requested as an alternative that the court delay the trial “to allow the passions and prejudice to fade,” his attorneys wrote in the court filing.

The securities-fraud trial is scheduled to begin Jan. 17. The presiding judge agreed Saturday to hold a hearing on the motion to transfer the trial’s venue on Jan. 13.

Write to Patience Haggin at patience.haggin@wsj.com