The Rockefellers, the founding family of Standard Oil, which later became Exxon Mobil, will have a news conference Wednesday to explain their position, The Dallas Morning News reported Tuesday.
Their view, that the chairman and chief executive officer positions should be held by two people, is a concern "held by multiple generations of their family," a press release issued by family members said.
Currently, Rex Tillerson holds both jobs.
An Exxon Mobile board statement says board members should make that decision, which will be put to a shareholder vote
Director of Ram Trust Services Bob Monk sponsored the resolution to split the jobs to help the company broaden its interests.
"It's a company that, whenever it has tried to diversify outside of its traditional businesses, has made a complete flub of them," Monk said.