“I was surprised that we are playing in Manchester and we had a referee from Greater Manchester”
Brendan RodgersSpeaking straight after Boxing Day's game
The FA will seek Rodgers' observations before deciding whether to act, and the Liverpool manager must respond by 2 January.
He defended his comments at his press conference on Friday ahead of Liverpool's Premier League match away to Chelsea.
"I certainly wasn't questioning the integrity of referees," Rodgers said. "It was more than logical [to question] having a referee from that part of the world [get] a game in Manchester."
After the match at the Etihad Stadium, Rodgers was angry that Raheem Sterling had a goal wrongly ruled out for offside and felt Luis Suarez was denied a late penalty.
Rodgers said: "Hopefully we won't have a Greater Manchester referee with Liverpool-Manchester games in future.
"We had nothing that went our way at all."
Bolton is only 16 miles away from the Etihad Stadium, and Rodgers said: "I was surprised that we are playing in Manchester and we had a referee from Greater Manchester.
"I was surprised when I saw it but that's by the by.
"For Liverpool against Manchester City, I don't think we'd get an official from Wirral."
Analysis - Former Premier League referee Graham Poll
"Referees accept it is a matter of opinion as to whether you have a poor performance. That is part of parcel of the game.
"What you mind is when people imply bias and question your integrity. Given how sensitive things are with alleged match-fixing, managers need to be more careful with what they say after matches.
"When you move up the professional leagues and into the Premier League, every season you are asked: Is there any team you feel you shouldn't referee because you feel it would affect your impartiality?"
The FA must decide whether Rodgers is in breach of rule E3 (1), which deals with comments made about a match official which could be argued imply bias, attack the officials' integrity or are personally offensive in nature.
Liverpool were top of the Premier League at the start of Boxing Day, but dropped to fourth after City's comeback victory.
Manuel Pellegrini's side fought back from Philippe Coutinho's opener to move within a point of leaders Arsenal after goals from Vincent Kompany and Alvaro Negredo.
The defeat for Liverpool leaves them three points adrift of Arsenal,
who beat West Ham,
with City second and Chelsea third.
Rodgers was particularly infuriated by the decision against Sterling, who put the ball in the net after being incorrectly flagged offside when the game was still goalless.
He also claimed Suarez had his shirt pulled by Manchester City defender Joleon Lescott inside the home penalty area in the late stages.
"I never go on about officials but I thought they were horrendous," he said.
"The linesman gave Raheem offside in the first half but they were not even on the same cut of grass. If you are working at this level, you have got to get those right.
Manchester City boss Manuel Pellegrini praises goalkeeper Joe Hart's performance
"I'm asking young players to make those runs, he does it perfectly, and is given offside.
"There was another incident in the second half when Luis should have had a free-kick on the edge of the box and arguably there was a penalty late on.
"Luis can't jump because (Lescott's) tugging at his shirt."
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