There have been protests and boycotts around the world prompted by Musk's outspoken and controversial political involvement.
He has been heading up President Donald Trump's Department of Government Efficiency (DOGE) initiative to cut federal spending and slash the government workforce.
On Wednesday, Politico reported that Trump had told his inner circle Musk would be stepping back from the administration in the coming weeks.
Shortly after the report was published, Tesla's share price turned positive.
The White House shot down the report as "garbage". Because he is considered a special government employee, Musk by law can only serve 130 days in the administration this year, which would put his departure closer to June.
The Tesla boss is the world's richest man and contributed more than a quarter of a billion dollars to help Trump get elected in November.
In recent weeks, he poured millions into a Wisconsin Supreme Court race, supporting former Republican attorney general Brad Schimel who was soundly defeated on Tuesday.