The website, Mediapart, which based its allegations on the so-called "Football Leaks' documents, claimed PSG had until the spring of 2018 asked recruiters to record the origin of players in four categories: "Francais" (French), "Maghrebin" (North African), "Antillais" (West Indian), and "Afrique noire" (Black African).
It is against French law to collect personal data which reveals racial or ethnic origins of individuals.
In 2014, the director of the club's recruitment unit across the country, excluding the Paris region, defended at a meeting the ethnic vision of the team, justifying a discriminatory recruitment policy, Mediapart said.
The comments triggered protests at the club, but despite being summoned by management, the director was never punished, Mediapart said.
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Qatari-owned PSG acknowledged and condemned on Thursday the existence of the ethnic identity files.
"The general management of the club never knew of an ethnic registration system within a recruitment department or possessed any such forms.
"Paris Saint-Germain confirms that forms with illegal contents were used between 2013 and 2018 by the recruitment cell of the training academy dedicated to regions outside Ile-de-France (Paris area). These forms were an individual initiative of the head of this department," it said.
In a statement, the LDH said any such system was deeply racist and discriminatory.
"These practices, if confirmed, are illegal," it said. "This is why the Human Rights League has decided to file to the public prosecutor a complaint ... to punish the culprits."
France's Sports Minister Roxana Maracineanu warned of consequences and said she had asked French football authorities to investigate the case.
"If this is proved true, they are punishable by disciplinary or even criminal punishment. It is not acceptable that people are identified and recruited according to their skin colour or origin," she said.
If found guilty those responsible could face five years in jail and a 300,000 euro fine.
It is not the first time the issue has come up in French soccer. In 2011, Mediapart revealed that the national coach at the time, Laurent Blanc, had discussed with other officials a project to enforce racial quotas in youth academies.
(Reporting by John Irish, Jean-Baptiste Vey and Julie Carriat; Editing by Richard Balmforth)
