But the ex-21st Century Fox CEO isn't a lock just yet.
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James Murdoch, ex-CEO of 21st Century Fox, is leading the race to replace Elon Musk as chairman of the Tesla board, according to a report from the USA.

Reporting from the Financial Times, citing two people briefed on the discussions, places Murdoch ahead of Antonio Gracias, a long-time investor in the company and current lead independent director.

The report also says external options are also being considered. Tesla, Murdoch and 21st Century Fox haven't provided comment on the matter.

Musk is stepping down from his chairman role as part of a settlement with the US Securities and Exchange Commission (SEC), which was investigating him over tweets about taking Tesla private. He's still CEO, however.

In August, the controversial entrepreneur said he was "considering taking Tesla private" with "funding secured" at US$420 ($580) per share. The tweets were "false and misleading" according to the SEC, because Musk hadn't discussed or confirmed key terms of the deal before announcing it.

Reporting has suggested the tweets, which caused "significant" disruption to the market, was based on a 20 per cent premium over where the stock was trading before Musk's announcement – although pop-culture outlets have suggested it was a 'weed joke' designed to impress Grimes, Elon Musk's girlfriend.

The SEC highlighted the impact Musk has on the market, and made a point of holding him to the same standards as other corporate officers, regardless of his celebrity.

“Corporate officers hold positions of trust in our markets and have important responsibilities to shareholders,” said Steven Peikin, co-director of the SEC Enforcement Division.

“An officer’s celebrity status or reputation as a technological innovator does not give license to take those responsibilities lightly.”