The governing body has the right to appeal against the length of the ban in the same way the Chelsea centre-back may challenge the ruling, The Sun reports.
"We act as the prosecution in these cases and if we do not agree with the Commission's findings we have the right to appeal just like the defendant," an FA source told the newspaper.
"Admittedly it is something that is done very rarely but it is an option open to us."
Both parties are currently awaiting a full report from the independent commission that carried out the investigation, which will explain the length of the ban.
Terry, who was cleared of the same offence in court over the summer, was also hit with a £220,000 fine.