Manchester City defender Thatcher made a reckless challenge on Mendes' face as the duo was chasing the ball on the touchline in the Premiership clash on Wednesday.
Thatcher was shown a yellow card following the incident, but the FA are looking to take further disciplinary action although it contradicts the rules.
"We are looking at whether this may possibly be an exceptional case and what options may exist under our disciplinary regulations," an FA spokesman told BBC sport on Thursday.
"It is one of the fundamental rules of the game that the referee's decision is final. Therefore, if it is his decision that an offence warrants a yellow card, that cannot be changed later."
Manchester City have issued a statement on their official website confirming that Thatcher apologized to Mendes.
"Thatcher has personally written a letter to Pedro Mendes to apologise to him following the tackle in the match last night."