Shares of the Irving, Texas, company at last check were down 3.5% to $43.60.
Between 5% and 10% of U.S.-based employees who are subject to performance evaluations could end up leaving this year after their assessments, Bloomberg reported.
An Exxon Mobil spokesperson said in an email that "we currently have no plans for layoffs, and there are no targets to reduce headcount.
"ExxonMobil manages the highs and lows of the industry cycles by supplementing our employees with contractors," the company said in a statement. "As we head into down cycles, we reduce the use of contractors. That is happening now. We have a rigorous talent management process which routinely assesses employee performance."
Last month, Exxon Mobil posted a surprise first-quarter loss amid a historic decline in global crude prices and said it would slash spending by $10 billion in order to protect its dividend and balance sheet.
The company said it would slash its 2020 capital spending plans by around 30%, to $23 billion.
Chief Executive Officer Darren Woods said the coronavirus "significantly impacted near-term demand, resulting in oversupplied markets and unprecedented pressure on commodity prices and margins."
Woods told Exxon Mobil’s annual meeting that while no were layoffs planned, the company was reducing its number of contractors and is trying to become leaner.
Exxon Mobil employed 74,900 people worldwide at the end of 2019.