If he did, Mayne-Nicholls would be the third candidate in the race with the incumbent and overwhelming favourite, 78-year-old Swiss Sepp Blatter, and former FIFA deputy secretary general Jerome Champagne, a 56-year-old Frenchman.
Mayne-Nicholls, 53, is the former head of the Chilean FA and was in charge of the technical investigation which evaluated all the bids for the 2018 and 2022 World Cups.
He told Reuters on Wednesday: "I am actually evaluating the situation. It is a very good idea but I must be careful with the decision.
"If I decide to stand it will not be as a testimonial candidature, I will give my best efforts to win, that will be my goal."
He continued: "In my opinion, the best for FIFA's future will be to have as many candidates as possible.
"Then we will be able to discuss ideas; to exchange opinions; to look forward to the changes the organisation needs. As well as those aspects, we will bring back "democracy" and that is the main key to having more transparency in football."
Mayne-Nicholls was the first senior official to openly warn against playing the World Cup in the summer heat of the Gulf, and the Qatar bid was ranked bottom of those competing for the finals behind the United States, Australia, South Korea and Japan.
He needs to get the backing of at least five national federations to be eligible to stand for the presidency and if he won he would be only the second non-European president of FIFA since it was formed 110 years ago. Joao Havelange of Brazil, president from 1974-1998 was the other one.
Mayne-Nicholls indicated his intention in a newspaper column in Spain and also told keirradnedge.com: "A decision is not necessary before January 28 next year. The election is on May 29, so we have all of October, November, December and January.
"That means four months to check everything so that the people who have contacted me -- and whom I have contacted -- can assess the best way forward.
FRESH AIR
"Once you decide to be a candidate, you have to convince 105 of 209 countries who are members of FIFA because that is what is needed to win," he added.
"I wrote a column a few months ago for El Pais in Spain in which I point out the need for fresh air. What has happened lately has not served the image of FIFA or, indirectly, football.
"There is a complete disconnect between what the fans think is needed and the administration of the game.
"That leads me to believe that you can accomplish change while maintaining what works well. I do not think it is wise, in the long term, to maintain both the same individuals and structures."
UEFA president Michel Platini, who has said he no longer supported Blatter's presidency, announced in August he would not run for the job, deciding to stay with UEFA instead.
On Monday, Michael Hershman, a member of the Independent Governance Committee which handled FIFA's reform process between 2011 and 2013, said it was time for Blatter, 78, to step aside.
Hershman said: "I think that president Blatter should resign for the good of the sport, and for the good of the organisation. He was in a leadership position when all of the scandals happened and he hasn’t taken personal responsibility.
"(Even) if it's true that he hasn’t been found to have been involved in personal wrongdoing, frankly, my experience has been that when you have organisations that are continually under a cloud, one of the most effective ways to get out from under that cloud is to change the leadership."
(Editing by Ken Ferris and Steve Tongue)
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