The Washington Post reported that an employee of the company said that staff would be subject to an HR investigation if they were to follow in the footsteps of Musk.
The question was posed in a message viewed by The Post, which said that an employee would likely be the subject of an investigation if they posted something on social media.
The inquiry came ahead of a question-and-answer session with Musk, which the CEO told employees about on Thursday, according to The Post.
A spokesman for the company told Business Insider that they can confirm that the company's CEO will join the employees for a question and answer session.
According to messages obtained by The Post, some employees were worried about Musk's new role on the company's board of directors.
A request for comment was not immediately responded to by Musk.
This is not a finished story. You can check back for updates.