Tesla CEO Elon Musk has given what appears to have been a costly interview.

Shares in the electric car maker tumbled over the weekend after CEO Elon Musk conceded that job stress may be getting the best of him in a newspaper interview.

It triggered a sell-off that knocked $US5.4 billion off Tesla's market value.

The interview led analysts and business professors to question whether Tesla’s board might grant Mr Musk leave or even replace him.

The New York Times report said Mr Musk exhibited both laughter and tears throughout the interview, acknowledging he sometimes works 120-hour weeks and takes Ambien to get to sleep.

“It's kind of bizarre,” said Charles Elson, director of the corporate governance centre at the University of Delaware.

“It's a drama we shouldn't be watching.”

Despite his stresses, Mr Musk said he will not give up his dual role as Tesla's chairman and CEO.

“If you have anyone who can do a better job, please let me know. They can have the job. Is there someone who can do the job better? They can have the reins right now,” he said.

Tesla's board does not appear to be taking any action.

“Over the past 15 years, Elon's leadership of the Tesla team has caused Tesla to grow from a small start-up to having hundreds of thousands of cars on the road that customers love, employing tens of thousands of people around the world, and creating significant shareholder value in the process,” the board said in a statement.

It is a tricky decision for the board because Mr Musk has been crucial to changing the perception of electric cars and dominates the company's public identity.

University of Michigan business and law professor Erik Gordon says Tesla’s board has a fiduciary duty to shareholders to take action.

“If the board does not get him out of this slot, at a minimum on a leave-of-absence basis, I think the board is going to be seen by a lot of people who love the company as being derelict in their duties,” Professor Gordon told reporters.

“You can love the company, you can love Musk and hate having him be the CEO at this point.”

The New York Times says the board is working in the background to find a No. 2 executive to relieve some of the pressure on Mr Musk.

The board has stood behind Mr Musk amid some bizarre recent behaviour, including labelling a diver who aided in the cave rescue of Thai soccer players as a paedophile, and tweeting about a funding deal that caught the attention of the US Securities and Exchange Commission.