Duo in racism row may be charged with bringing the game into disrepute.
English FA to finish its inquiry after Terry is cleared in the court
The English Football Association now has to conclude its own investigation and decide whether to charge Terry over his confrontation with Queens Park Rangers defender Anton Ferdinand, which led to the failed criminal prosecution.
Action could also be taken against Ferdinand, who - like Terry - admitted using obscene language during the Premier League match that led to the trial.
The FA had to suspend its investigation into October's west London derby when the police probe kicked in. However, the governing body's inquiry was restarted after the court decided there was no evidence to find Terry guilty of a racially-aggravated public order offence.
The FA, which stripped Terry of the England captaincy over the case, said its priority is to "conclude its own enquiries".
There is a lower burden of proof for FA disciplinary tribunals - balance of probabilities rather than beyond reasonable doubt in criminal cases.
And this puts the FA in a "difficult position" as it contemplates whether to act, according to Professional Footballers' Association chief executive Gordon Taylor.
The FA banned Luis Suarez, the Liverpool striker, for eight matches last season for racially abusing Manchester United defender Patrice Evra in another Premier League match in October.
And, even if the FA decides not to pursue the racism claims a court threw out, the governing body could charge Terry - and Ferdinand - with bringing the game into disrepute or misconduct for their foul and abusive language.
"There were normal verbal exchanges between the players during the game - however unpleasant, it's a fact of the modern game," Terry said in a police interview provided to the media. "I felt that QPR players were trying to unsettle us."
Taunting Terry over high-profile allegations of an extramarital affair, Ferdinand also made an "obscene gesture," as the Chelsea player described it. But chief magistrate Howard Riddle decided it was "impossible" to be sure what Terry said in the key exchange.
The FA has already interviewed Ferdinand and Terry.
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