The complaint was lodged in June by a witness who claimed Dean Ramsdale used offensive terms in a conversation.
This was passed on to Manchester City's legal and HR teams who began an internal investigation, which is still underway.
Ramsdale was told that such language would not be tolerated by the club.
A letter of apology has been sent to the person who first complained.
According to 'Sky Sports', Manchester City make all their staff undergo diversity training which is delivered by the FA, the Premier League and race relations agencies.