Blanc was reportedly among several officials at the French Football Federation (FFF) who discussed last November the introduction of quotas and was heard comparing the almost all-white Spanish team to the mixed-race French team.
An internal investigation into the claims has since been set up by the FFF.
Blaquart is under increasing pressure to quit his post after the Mediapart website accused him of producing a graphic chart highlighting the percentage of dual-nationality players who pass through France's coveted training programmes.
The website claims Blaquart lamented the fact that 40 to 50 per cent pof the players in the country's national youth teams are of dual nationality.
Mediapart says officials fear that players will benefit from professional coaching in France and then decide to play for other countries.
Blanc, the former France captain, is currently on holiday in Italy, but both he and Blaquart are expected to be summoned to a hearing next week.
French Minister for Sport Chantal Jouanno was unequivocal on the quota issue on Friday.
"A national training programme should be selecting the best players based purely on their physical and mental attriubtes, and no other criteria," she said.
The results of the internal investigation are expected Monday and Wednesday next week.