A leading presidential candidate of Mexico's ruling conservatives raised the possibility on Thursday of listing oil company Pemex on the stock exchange to help revamp the state-owned giant.

Josefina Vazquez Mota, who is bidding to become the first woman to serve as Mexican president, told Reuters in an interview the next administration needed to examine how Brazil had managed its partly privatized state oil firm Petrobras.

The case of Petrobras is a good reference point, not necessarily to copy it 100 percent, but it deserves particular attention, said Vazquez Mota, who is leading the race to be the candidate for President Felipe Calderon's National Action Party, or PAN, ahead of the July 1 election.

Oil production has dipped at Pemex, which has been dogged for years by allegations of inefficiency and corruption, prompting many Mexican lawmakers, particularly from the right and center of the political spectrum, to urge an overhaul.

Although many advocates of oil reform say Pemex needs private investment, they have shied away from discussing a potential listing for the company, which has been a sacred cow since Mexico nationalized the oil industry in the 1930s.

It's one of the scenarios, not the only one, Vazquez Mota, a former education minister and ex-PAN congressional leader, said of floating Pemex on the stock exchange. In the end, the most important thing isn't whether to list Pemex or not, that could be the result of many prior decisions.

In August, three private companies won the first contracts to operate mature oil fields in a bid to modernize the oil industry. Pemex says the number of fields operated by private firms will jump by the end of 2012.

SLAMS 'MACHO' RIVAL

Key reform projects like an overhaul of the labor market, taxation and Pemex have been stymied by the fact no ruling party in Mexico has had a congressional majority since 1997.

Vazquez Mota, 50, said she would push for the presidential candidates to seal a joint political accord before the election pledging their commitment to support the four or five major reform drives.

The PAN plans to pick its candidate by February 5, although the main opposition Institutional Revolutionary Party, or PRI, and the leftist Party of the Democratic Revolution, or PRD, have already settled on their presidential nominees.

Leading the opinion polls is PRI candidate Enrique Pena Nieto, former governor of the state of Mexico.

But his campaign suffered a setback this month when he struggled at a book fair to name three books that influenced him, and upset a number of women with a throwaway remark.

I'm not the woman of the house, Pena Nieto said after failing to identify the price of staple foodstuff tortillas, sparking condemnation on online social networks.

Vazquez Mota, a mother of three, called Pena Nieto's comment embarrassing, macho and very misogynist, saying it reflected authoritarian attitudes within the PRI, which ruled Mexico for 71 years until 2000.

Worse still, she said, was the fact that the string of gaffes showed Pena Nieto was not competent to run the country.

If you don't have an answer to the most basic thing, or if the answer puts down your own citizens, I think we're in an extremely risky situation, Vazquez Mota said.

(Editing by Peter Cooney)

Mexico