MEXICO CITY—Three independent board members of state-run Petróleos Mexicanos are set to resign over discord with President Andrés Manuel López Obrador’s strategy for managing the troubled oil firm, say people with knowledge of the situation.

The departures could give Mr. López Obrador tighter control over Pemex as he seeks to shore up the state firm’s dominant role in an oil industry that was opened to private and foreign investment in 2013 as part of a broad energy sector overhaul that he opposed.

Board...