Still, Musk told the Times that he has no plans to 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 told the paper.
Tesla's board showed no sign of taking any action Friday. In a statement to The Associated Press, the directors — excluding Musk himself, who is board chairman — praised Musk's dedication to the company.
"Over the past 15 years, Elon's leadership of the Tesla team has caused Tesla to grow from a small startup 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 statement said, without addressing Musk's recent behavior.
The Times interview puts board members in a difficult position because Musk, who entered Tesla as a major investor and built the company into a force that has changed the perception of electric cars, is the company's public identity.
But Erik Gordon, a University of Michigan business and law professor, said 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," Gordon said Friday.
"You can love the company, you can love Musk and hate having him be the CEO at this point."
The board has stood behind Musk despite some bizarre behaviour. For instance, in a recent tweet he labeled a diver who aided in the cave rescue of Thai soccer players as a pedophile. He later apologised.
But a tweet Musk fired off last week has reportedly made him and the directors the targets of securities regulators, and may force the board to act.
Musk tweeted that he had "funding secured" to take Tesla private and avoid the quarterly earnings pressures from Wall Street. The out-of-the-blue announcement raised a huge ruckus and pushed Tesla's shares up 11 per cent in a day, boosting the company's value by US$6b.
There are multiple reports that the US Securities and Exchange Commission is investigating the disclosure, including asking board members what they knew about Musk's plans.
Experts say regulators likely are investigating if Musk was truthful in the tweet about having the financing set for the deal.
In the interview, Musk stood by the tweet. But he told the newspaper that he wrote the tweet inside a Tesla Model S while he was driving to the airport, and that no one else reviewed it.
Asked if he regretted it, he said, "Why would I?"
In a separate report, The Wall Street Journal said securities regulators have been investigating if Tesla misled investors about Model 3 production problems.
The company could face sanctions if regulators find it did not accurately portray production delays to investors.
At a normal company, Musk would have been replaced already, Elson said. But Tesla isn't quite normal, with the identity and success of the company tied directly to Musk's intelligence and personality.
Most of the company's board members have ties and relationships with Musk, but Elson and Gordon say they also have a fiduciary duty to all the other shareholders. Musk owns about 20 per cent of the company.
"At some point the board is going to have to assert its authority," Elson said. "They're at a point where they're going to have to distance their oversight from any prior relations."
The Times cited people familiar with the situation as saying the board has been trying to find a No. 2 executive to help relieve some of the pressure on Musk.
Gordon said the board has to act now or be open to shareholder lawsuits. He suggested replacing Musk as CEO and keeping him on as a visionary chief technical officer.
The interview and other actions, Gordon said, are signs that Musk no longer can handle the CEO job. Musk spent nights at Tesla's Fremont, California, factory working out production problems on its new Model 3 car that is supposed to take Tesla from niche luxury carmaker to a mass producer that competes with Detroit.
But Gordon said a CEO wouldn't live at the factory. Instead, he or she would form a team to work overnight and solve problems.
The company said the board formed a special committee to evaluate proposals to take the company private. It later disclosed that Musk had talked with the Saudi Arabia government investment fund about the deal.
Some of Musk's stress comes from critical short-sellers who are betting against the company's success. But much of it comes from Musk's own pronouncements, such as lofty goals for production of cars or turning a sustained profit starting this quarter, that might be beyond reach. Tesla has never made money for a full year and has had only two profitable quarters since it went public in 2010.
- AP