Elliott Management Corp. is readying for a potential new fight with Hess Corp., hoping to either remove John B. Hess, its billionaire second-generation chief executive, or push him to consider selling all or part of the energy company.
Elliott, which owns a 6.7% stake in Hess, is also seeking changes in how the company approaches shareholder returns, pushing for a dividend cut in favor of stock buybacks, people familiar with the matter said. The activist has told the company its concerns.
Other big investors who asked to remain anonymous said they have pushed for improvements in profitability, and believe Mr. Hess's leash is short as he seeks time to develop one of the biggest oil-and-gas finds in decades.
The hedge fund and the oil-and-gas company, both based in New York, fought a nasty battle in 2013 that led to Mr. Hess giving up his role as chairman and added Elliott nominees to the board. That fight, which settled on the eve of the vote, helped spur the sale of some Hess assets, including its brand-name gas stations.
Since then, the stock has underperformed, including slumping heavily this year. Shares of Hess have lost 30% in 2017, including dividends, despite a 21% rally in the S&P 500 and a 14% gain in oil prices. It has fallen about 35% since the 2013 settlement, compared with a 77% rally in the S&P 500 over that time.
"As long-term shareholders in Hess, we are frustrated by the company's continuing underperformance," Elliott portfolio manager John Pike said in a statement to The Wall Street Journal. "Shareholders are getting impatient because the changes needed to remedy Hess's severe undervaluation are substantial and need to be announced without delay."
Hess has sold more than $3 billion in assets this year, and executives met with more than 50 major shareholders in recent weeks who were supportive of its strategy, Mr. Hess said in an interview.
"The board and our leadership team is open to anything to optimize the portfolio, as is evidenced by what we have done in the last year," he said. "I don't think there's an oil company that has done more to reshape the portfolio than we have."
James Quigley, Hess's chairman, said in an interview that "John has the clear, unanimous and unambiguous support of our board as our CEO."
A fight over Hess could hinge on sentiment about multibillion-dollar oil and gas projects that investors are growing impatient with, and whether Mr. Hess can keep the support of his shareholders after 22 years at the helm.
In 2015, Hess, along with Exxon Mobil Corp., announced a giant oil discovery off the coast of Guyana. Some analysts have suggested Hess's share of it may be worth more than $6 billion; Hess's current market capitalization is about $13.5 billion.
Hess executives said recently the company won't generate free cash flow through 2020 because of investment needs tied to the Guyana discovery as well as the boosting of production from shale assets. Investors haven't been pleased with that time frame.
Elliott has been working with investment bankers to determine interest from potential buyers for the company or assets, such as its Asian offshore acreage or its U.S. shale plays, and it has also tapped recruiting firms to suggest candidates for chief executive and the board, some of the people familiar with the matter said.
Such steps are typically preludes to a board fight, which Elliott has until March to launch for Hess's 2018 annual meeting.
Mr. Hess, the company's biggest investor with more than a 10% stake, has long maintained a tight grip on the firm his father Leon started in 1933 as an oil-delivery company. The younger Mr. Hess took over as chairman and CEO in 1995.
Any fight over his future would be the latest example of activists targeting CEOs directly, battles that have tended to turn particularly personal, including one that Elliott had over the aerospace-parts company Arconic Inc. this year that led to the departure of Klaus Kleinfeld.
Mr. Hess has fashioned a strategy of using cash flow from producing assets in the Gulf of Mexico and Malaysia to finance growth in its shale business in North Dakota, as well as the Guyana development. Since 2007, Hess has spent $10 billion more on new investments and dividends than it generated in cash from operations, according to FactSet.
Elliott has proposed selling the Asian assets and even a stake in the Guyana asset, the people said.
The activists also believe Hess's dividend could be cut both to fill in for any cash flow lost from an Asian sale and because they believe the company would be better off buying back billions of dollars in a stock they think is undervalued, the people said.
Unlike many smaller U.S. oil companies, Hess has consistently paid a large dividend relative to its size. Since 2012, the company has paid $1.6 billion in dividends to shareholders, and Mr. Hess has received more than $150 million of that, according to FactSet.
Recently, Hess has used asset sales to help fund a $500 million stock buyback and development costs in Guyana.
"We view the steps Hess management has taken to reposition its portfolio to adapt to its transformational opportunity in Guyana as positive," Bank of America analyst Doug Leggate wrote in an October note to investors.
Write to David Benoit at david.benoit@wsj.com and Bradley Olson at Bradley.Olson@wsj.com