Billionaire investor Paul Singer, founder of hedge fund Elliot Management, is seeking to replace Twitter CEO Jack Dorsey, a source familiar with the matter told CNBC on Friday.

Twitter is one of the few US technology companies that one of its founders heads, but does not control. It gave shareholders equal voting rights, making Dorsey, who owns only about 2% of the company, subject to exchange from an active investor like Elliot.

The source said that Elliot was pushing for Dorsey, 43, to be sacked because his attention was divided between Twitter and Square, a mobile payment company he co-founded, and his desire to move to Africa and continue his business from there.

Twitter shares fell last year when the company revealed that its site encountered some errors that hampered its ability to target ads and share data with partners.

The reluctance of the San Francisco-based company to expand beyond the current site and its services has also left it with limited capabilities, compared to its larger social media counterparts.

The sources said that the Elliot Fund will seek to install its candidates on the Twitter board of eight members when three of the company's directors run in the next annual shareholders meeting.

It is not clear who Dorsey's alternative is Elliott is seeking to put him in the leadership position and the size of his Twitter share. The New York-based hedge fund has more than $ 40 billion in managed assets and has targeted major companies in recent months, such as SoftBank and eBay, and it also owns Italian football club AC Milan.

Elliot officials declined to comment, and no Twitter officials have spoken about it.

Investors were dissatisfied when Dorsey became Twitter CEO for the second time in 2015, but his November announcement that he wanted to move to Africa for up to six months added to the debate among investors about his management.

Dorsey, who founded Twitter in 2006, was the first CEO until 2008, when he was replaced by one of the founders, Yves Williams.

Williams accused Dorsey at the time of being a managerless manager and not keen on Twitter's profitability.

Dorsey returned as a temporary CEO after his predecessor, Dick Costolo, stepped down, as Dorsey's knowledge of the company and its rapid launch of new products helped persuade Twitter's board of directors to hand him over again.

Dorsey is not the first CEO to run two major companies. Steve Jobs has led Apple and the animated film studio with a breaker for years, while Elon Musk runs Tesla Electric Vehicles and the SpaceX rocket maker.