French daily Le Monde's Web site (www.lemonde.fr) reported on Thursday that Pereiro, who finished second behind American Floyd Landis, twice tested positive for the banned substance salbutamol which is used for the treatment of asthma.
However, Le Monde added that the Caisse d'Epargne rider had an exemption from the sport's governing body, the International Cycling Federation (UCI), to use the substance.
AFLD president Pierre Bordry told L'Equipe on Thursday: "This rider tested positive twice. Once in Gap and another time in La Toussuire.
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"Each time, he wrote on the test report that he had a TUE (Therapeutic Use Exemption). But I am asking him to provide us with the medical elements that justify him taking salbutamol."
Tour champion Landis tested positive for the male sex hormone testosterone during the race and is likely to be stripped of his title and banned for two years if he fails to prove his innocence at an appeal hearing.
As runner-up to the American, Pereiro would expect to be awarded the victory if Landis is unsuccessful.
Mathieu Desplat, a spokesman for Tour organisers the Amaury Sport Organisation, told Reuters on Thursday: "We are waiting until Jan. 25 when Pereiro's case will be reviewed by AFLD before taking any action".
Neither Pereiro, the Caisse d'Epargne team nor the UCI were immediately available to comment.
The director of Spain's government-run Sports Council Rafael Blanco told Spanish media: "From our point of view this isn't a positive test and Spanish authorities have not received any communication about any positive.
"The whole thing seems to have occurred because of a conflict in responsibilities between two institutions (in France).
"If there had been any doubt about the authorisation to take such substances then they make the checks immediately and if there had been the slightest suspicion about Pereiro they would already have made that clear."
Last year's Tour de France was marred by doping problems. A day before the start, nine riders were kicked out of the race over a blood doping scandal that had erupted in Spain in May.
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