One of Wall Street’s most powerful activist hedge funds has taken a stake in Twitter and intends to shake up the social network — including by potentially calling for the replacement of its founder, Jack Dorsey, as chief executive, two people briefed on the matter said Saturday.

Elliott Management, the roughly $40 billion hedge fund run by billionaire Paul E. Singer, has amassed a significant stake in recent months, which one of the people said was worth about $1 billion. It nominated four candidates for Twitter’s board ahead of a deadline last Sunday to name potential directors, the two people added.

Though Elliott has a number of concerns, its biggest is the fact that Dorsey is the chief executive title at both Twitter and another business he founded, the financial company Square, one of the people briefed on the matter said.

Dorsey’s divided attention has been a longstanding area of concern for investors in the technology company, whose business and stock price have grown in recent years — but more slowly than its social media competitors.

In the fourth quarter of last year, Twitter generated more than $1 billion in revenue, a first for the company. It earned $885 million during the quarter, up 12% from the same time in 2018. And the number of users who see ads on its platform on a daily basis grew 26 million in 2019, up 21% from the prior year.

But investors have complained that Twitter has failed to come up with innovative new products. Though its core social network remains prominent — it is one of President Donald Trump’s primary bullhorns — upstart rivals including, most recently, TikTok, have seized the public’s imagination and eyeballs.

In October, Twitter’s shares fell more than 20% when it reported that it has missed Wall Street’s revenue expectations. (The company expects to stage a recovery this year, with major events like the Olympics and the U.S. presidential election drawing users and advertisers to its service.)

More of Dorsey’s wealth is concentrated in the financial company Square. He owns about 13% of the company’s outstanding shares, a holding worth about $4.9 billion as of Friday, while he controls about 2% of Twitter’s outstanding shares, worth about $531 million.

Dorsey was also not a regular presence at Twitter’s San Francisco office for much of last year, making it a point to travel the world, including to visit more than 30 of Twitter’s global offices.

He also took a personal trip to Africa, where he met with local entrepreneurs to discuss the potential of cryptocurrencies there. As he returned from the trip in November, Dorsey announced his intent to live in Africa for three to six months during the summer of 2020, but added he had not yet selected a country.

In an earnings call earlier this month, Dorsey said that Twitter would move to decentralize its workforce because gathering the majority of its employees in San Francisco “is not serving us any longer.”

Dorsey has defended his travels, saying on the call, “We are a global service that requires global perspective.”

It is unclear whether Elliott’s concerns would be allayed by Dorsey giving up the chief executive job at Square and forgoing his plans to live in Africa — or whether Dorsey would seriously consider doing either.

Twitter lacks a crucial defense against activist shareholders that Silicon Valley peers like Facebook and Google enjoy: It has only one class of stock. That means Dorsey has no special super-voting shares that give him outsize control of the company, leaving him vulnerable if enough shareholders side with Elliott.

But Twitter is helped by the fact that only three of its directors are up for reelection in any given year, making it impossible for an activist investor to quickly seize a majority of board seats.

For now, the talks between the two sides are constructive, the two people added.

A spokesman for Twitter declined to comment on Elliott’s plans, which were reported Friday by Bloomberg News.