After offering to buy Twitter outright for $41 billion (£31 billion), Musk looked set to take over the social media giant completely.
However, investment company The Vanguard Group has upped its stake in Twitter to 10.3%, overtaking Musk’s 9.1% share.
The asset firm is now Twitter’s largest shareholder, although Musk is still the largest individual stakeholder.
Analysts for the Wall Street Journal believe the move will make a sale to Musk less likely, as the Vanguard Group “often sides with management on voting issues and doesn’t advocate for changes like a hedge fund or activist investor might.”
Musk wanted to take over Twitter in order to unlock its “extraordinary potential.”
In an offer letter to Twitter chairman Bret Taylor, Musk said: “I invested in Twitter as I believe in its potential to be the platform for free speech around the globe, and I believe free speech is a societal imperative for a functioning democracy.”
He added: “My offer is my best and final offer and if it is not accepted, I would need to reconsider my position as a shareholder.
Musk is one of Twitter’s most popular users, and recently bought a 9.2% share in the social media company after making a series of controversial polls about the platform’s future.
On Twitter, Musk asked his followers if the platform should add an ‘edit’ button to posts, or if he should turn Twitter’s San Francisco headquarters into a homeless shelter.
He even asked them if he should remove the ‘w’ from Twitter’s name, with 55.8% of respondents voting ‘yes’.
After becoming the company’s largest shareholder, Musk announced he would not be taking up a seat on the company’s board of directors despite it being offered to him.
Twitter CEO Parag Agrawal said it was “for the best”.
He said: “We have and will always value input from our shareholders whether they are on our board or not. Elon is our biggest shareholder and we will remain open to his input.”