The board has not engaged in any "serious" discussions of who should be the chairman, the paper said, citing a source close to the selection process.
But the deal didn't prevent the free-wheeling Musk from continuing to speak out about other subjects - a liberty he took advantage of to bash the SEC today in a tweet that indicated he is still stewing about the allegations filed against him.
Tesla was not available for comment to CNBC or the Wall Street Journal.
Just in case there is any confusion, Shortseller Enrichment Commission is a jab at the Securities and Exchange Commission. Unbelievable as it may sound, the $40 million fine and losing the chairmanship of Tesla doesn't seem to have done much to deter Musk from speaking his mind over Twitter.
It's not an uncommon practice for a judge to ask for such a letter.
Tesla has consistently been one of the most-shorted USA stocks as many investors continue to bet on declines in share prices.
But Musk apparently was done venting about his frustrations with the securities market, taking aim a few hours later at the investors who are short selling his company's stock.
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"Seriously? You know you still need their help convincing a judge that your penalty was sufficient".
Updated at 5:25 p.m. PT with Musk's tweet about short sellers.
He has used Twitter to criticize short-sellers betting against his company.
Greenlight is having a hard year, with its main fund down 25.7 percent through September, but said its Tesla short position was its second biggest victor in the third quarter.
For her part, Nathan may have limited room to intervene, after a federal appeals court curbed the ability of judges to reject SEC settlements.
But in 2014, the 2nd U.S. Circuit Court of Appeals overturned Rakoff's rejection of a $285 million SEC settlement with Citigroup Inc, saying he should have given "significant deference" to the regulator.
"In and of itself it's not an ominous sign", said Jordan Thomas, a partner at Labaton Sucharow and former SEC lawyer.
"The Court has a duty to ensure the proposed consent judgment is "fair and reasonable", Judge Nathan wrote in the order, numbered 18-cv-08865-AJN". "The vast majority of settlements like this are approved by courts".