There’s a new boardroom battle in tech: activist investor Paul Singer vs. the enigmatic CEO of Twitter and Square, Jack Dorsey.

Elliott Management, the activist hedge fund run by billionaire Singer, has taken a nearly 5% stake in Twitter valued at about $1 billion, people familiar with the matter tell Yahoo Finance. The firm is now pushing for the ouster of Dorsey as CEO, and has nominated four members to Twitter’s board, sources say.

Bloomberg News first reported on Friday night a “sizable” stake taken by Elliott and the firm’s desire to send Dorsey packing.

Elliott is not agitating for a sale of Twitter, sources tell Yahoo Finance. (Twitter did hold talks to sell itself in 2016 to Google or Salesforce, and came very close to a sale to Disney, Bob Iger confirmed in his book last year.)

Rather, sources say Elliott believes Dorsey isn’t running the company correctly and that the board has been complacent. Elliott thinks Twitter could be worth significantly more with a full-time CEO running the ship and focusing on growing its ad revenue, sources say.

A decision on Dorsey’s fate may come quickly, as the two sides are already in talks, sources say.

A spokesperson for Twitter declined to comment to Yahoo Finance on the situation. Twitter shares (TWTR) jumped about 8% in trading Monday morning.

Elliott Management is hardly the first to question Dorsey’s ability to pull the double-duty of running both Twitter and Square, two publicly traded companies.

Over the past two years, the fortunes of those two tech players have diverged. While Twitter has taken heat for its failure to cut down on trolls and hate speech, Square has made strides in point-of-sale hardware and peer-to-peer mobile payments. Square was Yahoo Finance’s Company of the Year for 2018. Twitter stock is down 6% in the past two years, while Square shares is up 58%.

The criticism of Dorsey grew louder toward the end of 2019 when Dorsey announced last November that he plans to live in Africa for three to six months in 2020. Dorsey tweeted: “Africa will define the future (especially the bitcoin one!).” Dorsey’s obsession with bitcoin is no secret, and he has launched multiple bitcoin initiatives at Square, leading some to call it a distraction.

Jason Kint, CEO of the nonprofit trade group Digital Content Next, tweeted after Dorsey’s announcement, “This is the CEO of company mentioned 74x in [the] Mueller Report investigating Russia’s interference in 2016 US election. He’s moving to another continent for much of 2020 election??? And we’re [shrugging emoji] with this? WTF.”

In December, NYU Stern School of Business professor Scott Galloway, a Twitter shareholder and prominent voice in tech criticism, wrote an open letter to Twitter board chairman Omid Kordestani seeking for Dorsey to step down as CEO.

“A part-time CEO who is relocating to Africa? Enough already,” Galloway’s letter declared. “Twitter has, on every metric, underperformed peers for several years… This decline is despite the fact... that Twitter has become an iconic brand and the global heartbeat for our information age.”

Dorsey returned to run Twitter, the company he cofounded, in June 2015, when he was announced as interim CEO when Dick Costolo resigned. In October 2015, Twitter announced he would stay as permanent CEO. Since Dorsey returned, Twitter stock has severely underperformed its competitors.

Twitter stock is down 7.5% in that time, while Facebook is up 136%, Google is up 151%, and the S&P 500 has risen 41%. Square, Dorsey’s other company, is up 374%.

Elliott Management is sure to cite stock performance, among some more abstract recent headlines and events, to make its case with Twitter’s board. And Elliott’s timing is key, as Twitter has three board members up for re-election: Bret Taylor, Ngozo Okonjo-Iweala, and chairman of the board Omid Kordestani.

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Daniel Roberts is an editor-at-large at Yahoo Finance. Follow him on Twitter at @readDanwrite.

Brian Sozzi is an editor-at-large at Yahoo Finance and co-anchor of The First Trade. Follow him on Twitter at @BrianSozzi and on LinkedIn.

Read more about Dorsey’s leadership of Twitter and Square:

Jack Dorsey will face more pressure in 2020 to step down as CEO of Twitter or Square

Twitter CEO Jack Dorsey’s Twitter account gets hacked

Jack Dorsey’s love of bitcoin could cause problems for Square

Why Square’s embrace of bitcoin was ‘brilliant’

Square is Yahoo Finance’s 2018 Company of the Year

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