As part of the settlement, Musk will also step down as the company's chairman but remain as chief executive.
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.
Tesla did not immediately respond to requests for comment.
The SEC alleged that Musk hadn't locked up the estimated $25 billion to $50 billion that it would have required to pull off that deal, and wanted to punish him by forcing him out as Tesla's CEO.
The judge said it was her regular practice to request such letters. The agreement also requires Tesla to hire or designate a securities law attorney to ensure that posts made by Musk and other executives to Twitter follow SEC disclosure rules.
The tweet appeared to jar investors, who drove Tesla shares down 2.4 percent in after-hours trading to $275.
The SEC and Musk will probably argue that removing Musk as CEO could further harm the company's stock, and thus hurt shareholders, he said.
"Seriously? You know you still need their help convincing a judge that your penalty was sufficient".
Greenlight said it also sold its last Apple Inc shares in August at $228 per share, eight years after buying the iPhone maker at less than one-sixth that price, on growing fear of "Chinese retaliation against America's trade policies".
Musk continued his tirade against short-sellers by sending out another inflammatory tweet at 6:40 p.m.
His distaste for short sellers was viewed as a key reason why he briefly proposed taking Tesla private - a short-lived plan that he revealed on Twitter despite, the SEC said, not having lined up the funding he claimed to have gotten for the deal. A federal judge sought to rip up a settlement between Citigroup and the SEC in 2011, launching a three-year battle with the SEC.
Separately, the Wall Street Journal said billionaire businessman Mark Cuban talked with Musk for 15 minutes and convinced him to take the deal.
But the settlement still needs court approval.
"In and of itself it's not an ominous sign", said Jordan Thomas, a partner at Labaton Sucharow and former SEC lawyer. The court expects to receive the joint statement by 11 October, explaining why their settlement should be approved. "This is just a hoop to be jumped through".