Jurgen Klopp was sent off against Manchester City for berating a referee's assistant when a foul was not given
In a news conference following Liverpool's 1-0 win over City last week, the German was asked whether comments made before the match at Anfield were "borderline xenophobic".
Klopp had said the three clubs could "do what they want financially".
Senior figures at City were privately unhappy with those comments.
"In this specific case, I don't feel that at all," Klopp said.
"I know myself. You cannot hit with something which is miles away from my personality."
It is understood the FA's stance is backed up by anti-discrimination groups, who believe it would be difficult to prove City's claim.
They believe the fact there was no mention of race, ethnicity, nationality or culture by Klopp would support the German's defence of being related only to claims of perceived financial disparity and how it might affect the competitiveness of football.
Klopp, who has been charged by the FA for his touchline behaviour in the win over Manchester City, had said: "There are three clubs in world football who can do what they want financially. It's legal and everything, fine, but they can do what they want."
He added: "Newcastle [sporting director Dan Ashworth] said there's no ceiling for the club, he's right, there is no ceiling for Newcastle - congratulations, some other clubs have ceilings. We cannot act like them, it's not possible."
-- Courtesy of BBC Sport