But it added that the current status of the succession planning for the electric car-maker was not known.
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1:36
Musk jokes about attacks on Tesla cars
Tesla’s chair, Robyn Denholm, later reacted to the report by insisting that any suggestion of an active search was “absolutely false”.
She added that the board was highly confident in Musk’s ability to continue “executing on the exciting growth plan ahead”.
Musk’s net worth has plunged and Tesla stocks have fallen sharply amid a public backlash over his role in Donald Trump’s government. He owns just under 13% of Tesla stock and is the largest shareholder.
The world’s richest man has been leading the Department of Government Efficiency (DOGE), where he has overseen the firing of tens of thousands of government employees.
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He has also supported far-right parties in Europe, which has led to protests against Musk and Tesla, which have seen its showrooms and charging stations vandalised across the US and Europe.
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1:01
Musk pulls back from DOGE role
It comes after Musk said the time he spends with DOGE would “drop significantly” from May and he will dedicate more time to running his companies, such as Tesla, SpaceX and X.
The board members met with Musk and asked him to announce publicly he would spend more time at Tesla, the report said.
It was unclear if Musk, who is a member of the board, was aware of any attempts to identify a successor, or if his pledge to spend more time at Tesla had affected succession planning, it added.
On Wednesday, Mr Trump said Musk could be part of his administration for as long as he wants.
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“You’re invited to stay as long as you want,” Mr Trump said.
He said Musk had been “treated unfairly” for his role in helping Mr Trump slash the size of the federal government, adding: “You really have sacrificed a lot.”