Elon Musk is hoping an investment from Saudi Arabia's sovereign wealth fund can help take Tesla Inc. TSLA, +3.31% private, but it may strike an investment deal with a Tesla rival, according to a report Sunday. The fund, called PIF, is in talks to invest in electric-car startup Lucid Motors Inc., according to Reuters. The report said after an initial $500 million investment, PIF could eventually invest more than $1 billion and gain majority ownership of the Newark, Calif.-based company. Lucid was founded in 2007 by former executives from Tesla and Oracle Corp., and has received significant funding from Chinese investors. While it had not built any cars yet, it hopes to start production later this year.