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Paul Singer, the billionaire founder of the activist fund Elliott Management, is preparing a plan to try to replace Jack Dorsey as CEO of Twitter, according to a report Friday by Bloomberg.

Elliott, based in New York, has nominated four directors to Twitter's board and also seeks to make other changes at the company, Bloomberg said. According to the report, Elliott has a "sizable" stake in Twitter, but the exact size of the stake is unclear.

Twitter declined to comment. Elliott Management didn't immediately respond to a request for comment.

One reason Elliott is pushing for the takeover is because Dorsey's time is split between running two public companies, Twitter and the payments firm Square, according to CNBC, which also reported the news. Dorsey's desire to spend up to six months in Africa this year is also a concern for Elliott, the report said.

The news comes at a challenging time for Twitter, as the social network tries to deal with election disinformation, abuse and other problems with the platform.

Twitter's stock rose more than 7% in after-hours trading.