Cheryshev, who scored four goals in five World Cup games for Russia as they reached the World Cup quarterfinals, denied taking a banned substance following remarks attributed to his father, Dimitri, in a Russian publication last year.
The publication reported Dimitri Cheryshev as saying Villarreal staff had administered the growth hormone to treat an injury, but later said he had meant to refer to a legal substance “growth factor” and was misunderstood.
“We have opened an investigation to get more information regarding this case,” an AEPSAD spokesman told ESPN FC.
“We are investigating the case in collaboration with the Russian Anti-Doping Agency and we are in contact with the World Anti-Doping Agency.
“This case has emerged following the comments made by the player, Cheryshev, and his father. We want to know more information.
“We have started the process but it’s still early to draw conclusions. We don’t know how long this case will take.”
The Russian Football Union reportedly said the treatment Cheryshev had received had been a legal platelet-rich plasma injection.
Without a medical exemption, the use of growth hormone is considered doping and is punishable with a ban of up to four years.
Cheryshev joined Valencia on a a season-long loan from Villarreal earlier in the summer.