The Mexican government nationalized the oil industry in 1938. Hector Moreira, a member of the board state-owned Petroleos Mexicanos, told Bloomberg News that a "taboo" had been broken on privatization.
"People talking about private stakes -- it's a first step," said Moreira. "And it's a step that's not prompting a negative reaction from the public."
Presidential contender Enrique Pena Nieto and rival Josefina Vasquez Mota spoke in favor of at least some degree of privatization last week. Elections are July 1.
Mexico is one of the top oil-producing nations in the world. Though not a member of the Organization of Petroleum Exporting Countries, it's one of the top three exporters to the United States. Bloomberg notes, however, that without investments, Mexico might have to start importing oil by 2020.
U.S. and Mexican officials in February signed an agreement on the exploration of oil and natural gas along a shared maritime border in the Gulf of Mexico.
The agreement sets up a framework for U.S. energy companies to work with Mexico's state-run Petroleos Mexicanos to develop trans-boundary reserves that were off-limits under the terms of previous treaty agreements.