Elon Musk appears to have ruled out reports suggesting James Murdoch will replace him as Tesla Chairman.

Fox CEO and Tesla board member James Murdoch is apparently out as a prospect to replace Elon Musk as the battery-carmaker’s chairman.

Musk, who must relinquish the post as part of a settlement with the SEC, issued a Wednesday afternoon tweet declaring “incorrect” a report in the Financial Times that cited two supposed inside sources naming Murdoch as the frontrunner in the search. The FT story came days after several other media outlets also pointed to Murdoch as the likely successor.

The 45-year-old Murdoch is a friend of the Tesla founder and boss and has been on the company’s board since last year. He was seen as a particularly suitable replacement for Musk as he will soon relinquish his role as CEO of Twenty-First Century Fox, the media conglomerate founded by his father Rupert Murdoch, after it sells off most of its assets to Disney.

(Musk under fire again, this time from his supporters. Click Here for the story.)

The British business journal quoted one person it said was “briefed on the conversations” as saying, “The Tesla job is perfect for James, adding that Murdoch “will be sitting next to Elon…He’s going to get access to so much deal flow.” But in his tweet, Musk simply said, “That is incorrect.”

There has been some strong pushback to the idea of naming James Murdoch Tesla chairman.

Musk has been under pressure from critics to give up one of his two titles for several years. What finally forced his hand was the controversy over his August tweet declaring Tesla was set to go private at a stock price of $420 a share. The August 7^th posting indicated “Funding secured,” something that caused Tesla shareholders to wildly bid up the stock price for several days.

A week after the initial tweet, however, Musk backed down, indicating he came up with the idea after a meeting with executives from the Saudi Arabian sovereign investment fund and had no clear plan for privatization. He also appeared to have come up with the $420 number – “420” being common slang for marijuana —  to impress his girlfriend, according to comments made in an interview.

The Securities and Exchange Commission quickly launched an investigation and, late last month, sued Musk, alleging he made “false and misleading statements” to investors. On November 1, Musk moved to settle the complaint, paying a $20 million fine and agreeing to step down as Tesla chairman within 45 days.

(Tesla takes heat as Musk lashes out. Click Here for more.)

Whether Murdoch was ever in the running, as had been widely reported, is unclear. But critics found serious fault with the prospect of putting him in the Tesla chairman’s post. For one thing, the British-Australian businessman has had no experience in the automotive world beyond his brief tenure on the Tesla board. Some also had problems with Murdoch’s close friendship with Musk which, they suggested, might lead him to rubber-stamp the Tesla founder’s decisions.

Indeed, Murdoch’s bid for re-election was opposed by two prominent proxy advisory firms, Glass Lewsi & Co and Institutional Shareholder Services, as well as activist investment firm CtW Investment. Glass Lewis, in particular, asserted that Murdoch already served on too many boards, and had “a troubled history as an executive and director.”

It remains to be seen whether Tesla ultimately will turn to its current board for a new chairman or reach outside. Either way, the clock is ticking. Under the settlement with the SEC Musk must step down as chairman within 45 days. He does get to keep his primary job as Tesla CEO and he could seek to be re-elected as chairman after three years if he doesn’t again run afoul of the SEC.

To avoid that, supporters hope the deal will convince Musk to tone down what his been his increasingly erratic behavior which, in recent months, has seen him attack journalists and industry analysts, and even one of the divers involved in rescuing a youth soccer team trapped in a flooded Thai cave. The diver has since filed suit in both Los Angeles and London.

(Musk paying SEC $20 million fine, resigning as chairman. For the full story, Click Here.)

But Musk quickly dashed such hopes, late last week taking aim at the SEC, dubbing it the “Shortseller Enrichment Commission.” A number of observers have suggested his original privatization tweet was aimed at hurting the short-sellers who have become a particular thorn in the South African-born executive’s side.

If Musk won’t tone down his frequent tweets, both critics and allies alike appear to be hoping that whomever does come aboard as Tesla’s next chairman will be strong enough to rein in the executive’s itchy twitter finger.