El Amrani said on Friday it was impractical to make detailed examinations of every international player on the continent and that CAF trusted teams to follow the rules.
The issue was highlighted after Burkina Faso's place at the African Nations Cup was thrown into jeopardy two weeks before the start of the tournament by a protest from qualifying opponents Namibia.
The Namibians said that Burkina had fielded Cameroon-born defender Herve Zengue against them when he was ineligible and took their case to the Court of Arbitration for Sport (CAS) after CAF threw out their protest on a technicality.
CAS rejected the protest while, in the meantime, Burkina Faso left Russian-based Zengue out of their squad for the tournament, which starts on Saturday.
El Amrani would not comment directly on a report in World Soccer magazine that co-hosts Equatorial Guinea had over the past few years fielded players from Brazil, Colombia, Nigeria and Cameroon who were ineligible under FIFA statutes.
"I have no comments. If we work on the basis of rumours written in media reports, then we can just close the office," said El Amrani.
"We work (based) on the statutes and regulations, and on that basis every national team in this African Cup of Nations or any competition of CAF follows a strict implementation of rules when they register the players."
FIFA statutes state that, in addition to being granted citizenship, a naturalised player must have lived in his adopted country for at least five years before he can play for the national side.
El Amrani said FIFA's new electronic transfer system made it easier to check where players had been based over the years.
"There is a strict system as well with the FIFA TMS (Transfer Matching System) and all kind of different tools and there are passports as well issued by the governments," he said.
"The point is very clear for us; we have a structure and a legal framework and a competition framework which we work with, and accept those players with their given nationality.
"We cannot be expected to go and check every single player on the African continent to see if maybe he has been born somewhere else, it just doesn't make sense."
"It's not our role to do that. Our role is to make sure of the eligibility of those players."
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