Hedge fund Elliott Management is reportedly poised to wage a campaign to unseat Hess CEO John Hess or force a sale of all or part of the company.
Shares of Hess were up 6 percent in after-market trading.
Elliott Management, which holds a 6.7 percent stake in Hess, also wants the company to cut its dividend and instead buy back stock from shareholders, The Wall Street Journal reported on Thursday. Other big investors are also pressuring the company to make improvements, the paper reports.
Investors are reportedly unhappy with Hess's projection that it won't generate free cash flow through 2020 due to spending tied to its offshore oil project in Guyana and its U.S. shale fields.
Hess is primarily focused on oil and gas exploration and development, and is also involved in transporting and storing crude through Hess Midstream Partners.
"As long-term shareholders in Hess, we are frustrated by the company's continuing underperformance," Elliott portfolio manager John Pike told the Journal.
Shares of Hess are down 31.5 percent this year.
"Shareholders are getting impatient because the changes needed to remedy Hess's severe undervaluation are substantial and need to be announced without delay," Pike said.
Hess Chairman James Quigley defended Hess in a statement to the Journal.
"John has the clear, unanimous and unambiguous support of our board as our CEO," he said.
Hess and Elliott previously clashed in 2013 in a battle that ended with Hess giving up his role as chairman and Elliott nominees joining the board of directors, the Journal notes.