Five Serbia U21 players and the assistant coaches of both teams have also been charged.
The brawl occurred following England's 1-0 European Championship qualifying win on 16 October, with players and officials from both teams clashing on the pitch amid accusations of racist abuse from the stands towards England defender Danny Rose.
Serbian police did not give the names of the players charged but said they had "committed an act of violence during a sports event".
The FA has, however, yet to be contacted by authorities in Serbia.
"Further to the Serbian police announcement regarding charging English Under-21 players and staff, the Football Association can confirm it has not received any formal notification of any charges filed by the Serbian authorities," a statement read.
"We have not been made aware of any of the names of individuals connected with these charges and we therefore await further details and formal communication on these matters.
"Meanwhile we are in contact with the British Government for advice, as well as speaking with our colleagues at UEFA."
Both countries' football associations have been charged by UEFA over the incident, while the Serbian FA has also been charged over the alleged racist abuse.
The Serbian FA previously banned two of their players for a year for their part in the brawl, as well as two members of their coaching staff.