Musk said he is giving serious thought to building a new social media platform. He didn't give any information on what the social media platform would look like or how it would work.
The billionaire and electric car maker made the remark after saying that the social networking site doesn't allow for free speech.
Musk said on Friday that failing to adhere to free speech principles undermines democracy. He asked if a new platform was needed.
Free speech is essential to a functioning democracy, and Musk questioned if the social networking site followed this principle.
A CNBC request for comment was not immediately responded to by the company.
The CEO doesn't like the fact that his statements are scrutinized.
Musk was subpoenaed by the Securities and Exchange Commission after he asked his followers if he should sell 10% of his stock.
In February, Musk accused the SEC of harassing and chilling his right to free speech.
The SEC said last week that Musk's motion to quash was procedurally deficient and meritless.
Even if the court throws out the SEC agreement that requires Musk to get approval from other executives before he posts about the company, the regulator told the judge that Musk's posts about the company will still be a reasonable subject for government investigation.
Musk wouldn't be the first person to set up their own social media platform.
The Trump Media and Technology Group includes Truth Social, which was launched in February. Since January, Trump has been banned from the social media site.
Matt Navarra, a social media consultant, told CNBC Monday that there is a trend for wealthy individuals with a polarizing presence on social media to want to build their own platforms.
In an effort to lure people away from Facebook, Parler and Gettr have launched.
Parler was removed from the App Store after it was accused of inciting violence during the riots. The company made some changes that made it better detect and moderate hate speech.
It's not easy to build a buzzing social network.
Navarra said Musk would need huge financial capital and a team of experienced product managers and engineers to build a sustainable and popular social network. It also needs to have people who are interested in engaging with it.
Navarra said that most of the alternative social networks set themselves up to be the home of free speech, and that they are often home to users with the most extreme or politicized views.
The nature of these alternative platforms and the content that gets shared on them means they often struggle to attract advertisers and investors they need to keep themselves afloat.
In the past, Musk has claimed that he and his companies are working on exciting products for years into the future, but often, the proposed innovations aren't realized within the projected timelines.
Musk said at the April event that the company would have 1 million autonomously piloted vehicles on the road in 2020. These robotaxis don't exist.