The company is based in nearby Palo Alto, California.
Investors and analysts viewed PIF as a natural financing partner. His personal stake in Tesla is nearly 20 per cent.
However, a source who is familiar with PIF's strategy said it was not now getting involved in any funding process for Tesla's take-private deal. They said the board is also evaluating this option. If there is evidence that the financing wasn't fully locked down, Musk's claim would expose him to allegations of fraud, Coffee said. A spokesman for PIF was not immediately available for comment.
Tesla did not respond to a request for comment.
The complaint alleges violations of American securities law and was filed on Friday as a class action in federal court in San Francisco.
The class includes investors who bought Tesla shares as they were rising in the wake of Musk's tweet.
Short-sellers of Tesla's stock have faced increasing aggression from Musk over recent months, with the billionaire citing the lack of market support as one of the main reasons he wants to take the company private.
Musk has also said he would be looking to keep his ownership of Tesla at around 20 percent in a buyout deal, and that a special goal vehicle, like the one that exists at his aerospace company SpaceX, would allow Tesla shareholders to remain invested if they so choose. In a barrage of new tweets, he joked about "short shorts" being included in "Tesla merch", suggested several potential names for the "shorts", and asked his followers which "short shorts" are their favorite.
"When you have these grand-vision companies, the founders - these leaders - don't want to have some investors have control", Gene Munster, a managing partner at venture capital firm Loup Ventures said in a Bloomberg TV interview, talking about the idea that Musk wouldn't want to bring in any large new shareholders.