Elliott Management Corp. – an activist investor owned by billionaire Paul Singer – has plans to shake up the management at Twitter.

As reported by Bloomberg on Saturday, Elliott has taken a large stake in the social media messaging platform and, according to "people familiar with the matter," has plans to remove Jack Dorsey as chief executive.

The hedge fund has already nominated four directors to Twitter's board, the sources said.

Dorsey is also the chief of payments firm Square and has become a darling of the crypto community for his advocacy of bitcoin (BTC). He recently integrated a feature on Twitter that would display an icon for cryptocurrency if the #bitcoin tag was posted.

Dorsey has also set up a dedicated unit within Square to work on helping advance bitcoin's technology. Square's Cash App offers bitcoin services, which provided almost half its revenue in Q4 2019.

In his time as Twitter's commander-in-chief, though, he's seen criticism over his management style, with the platform failing in some people's eyes to be sufficiently innovative and focusing instead on its core messaging service.

Since Dorsey returned to lead Twitter in mid-2015, the firm's stock have dropped 6.2 percent. Facebook's, on the other hand, have risen more than 121 percent over the same period, as per the report.

Bloomberg's sources suggested that, with three board places to become available at the firm's next annual meeting, Elliott wanted to be sure to nominate enough candidates to fill the openings.

The investment firm has been in private talks with Twitter about its concerns, Bloomberg said.