The claims against Albert Benaiges, according to the Catalan daily Ara, stretch back to the 1980s and 1990s, when he worked as a PE instructor in the city's Les Corts district.
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Police have received one formal statement from a former student, with more likely in the following days.
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The 71-year-old denies the allegations.
Former players at the Barcelona academy, known as La Masia, where Mr Benaiges worked from 1992 to 2011, have made no claims, according to the publication.
Mr Benaiges has been accused of exposing himself to students at the school, touching youngsters, forcing them to undress in front of classmates, and showing them pornographic videos.
Mr Benaiges told Ara, "I have never hurt anybody, and if I have, it hasn't been on purpose." "My conscience is clear; I've never forced someone and I've spoken out against paedophiles."
Josep González Cambray, Catalonia's Minister of Education, announced on Saturday that his department has launched an investigation into the alleged abuses and has pledged to support all those who come forward.
Mr Cambray, in a tweet, stated that "School must be a safe environment free of all forms of violence. These conditions are untenable, and we must take decisive action ".
Mr Benaiges moved to the United Arab Emirates, Mexico, and Japan after leaving Barcelona in 2011.
Following Joan Laporta's re-election as president of Barcelona, Mr Benaiges returned to the club's academy early this year.
However, he quit the club last week for "personal reasons," according to club authorities. Ara stated that he had been fired the previous day.Ara said that he was fired the day after the club learnt of the probe by the newspaper.
The charges "shocked and astonished" first-team coach Xavi Hernandez, who told reporters about this.
Mr Benaiges oversaw the development of Barcelona's golden generation while in head of the academy, bringing players like Lionel Messi and Andres Iniesta through to the first team.