Many longtime Fox observers have noted that he has already been largely written out of the narrative as brother Lachlan Murdoch takes control of the slimmed-down remainder entity.
"Just want to that the Shortseller Enrichment Commission is doing incredible work", wrote Musk, a frequent critic of investors betting against the electric auto company.
Murdoch, at a recent Goldman Sachs event, spoke about working with Tesla and Musk. Tesla did not immediately respond to a request for comment. But Murdoch, the CEO of 21st Century Fox and the son of the media mogul Rupert Murdoch, has also faced blowback from shareholders in the past, with critics citing his lack of relevant experience.
James Murdoch has no manufacturing or automotive sector experience. The deal with the SEC eased uncertainty over Tesla's future because the agency's lawsuit initially sought to bar Musk from serving as an officer or director of a public company, a prospect that rattled investors. "What's exciting about the company and about Elon is the goals are so audacious", Murdoch said, as quoted in the FT report.
"The question when it comes to James Murdoch is, 'Is he the guy who'll be able to establish that level of authority with Elon Musk?'" asked Abby Adlerman, CEO of Boardspan, a corporate governance consulting company.
In July 2017, Murdoch became an independent director on the board of Tesla.
In May, proxy advisers Glass Lewis & Co and Institutional Shareholder Services and activist investor CtW Investment opposed the re-election of Murdoch to Tesla's board.
Murdoch now serves on the boards of Twenty-First Century Fox and News Corp. He also stepped down as chairman of Sky after its takeover by Comcast. He resigned from the board of Sky plc, just yesterday.
Glass Lewis research director Courteney Keatinge said on Wednesday that while Murdoch's departure from Sky could alleviate some concerns, the Tesla chairmanship would still require a big time commitment as the company faces pressures on many fronts.
"I would still have reservations about the time he would be able to allot to this", Keatinge said, referring to the possibility of Murdoch as Tesla chairman. The numbers 420 are significant in marijuana culture - as well as in the tweet that cost Musk his chairman post to begin with. However, the FT also cited an anonymous source as saying that "external options were still being considered".
Mr Murdoch is now chief executive of the United States media giant 21st Century Fox, but he will step down after the firm completes the sale of much of its business to Walt Disney.
Tesla is under scrutiny for failing to produce its Model 3 sedan quickly enough and in sufficient volume to meet customer demand.
"The proposed settlements in this case are fair", lawyers for the SEC, Tesla and Musk said in the filing.
Tesla has until November 13 to appoint a new chairman of the board as per the agreements made between the company and the US Securities and Exchange Commission.
With U.S. stock markets broadly lower, Tesla shares pared losses to trade down 1.8 percent at $257.96 shortly before the close on Wednesday.