It was reported in the wake of City's 4-1 triumph over Spurs, in which Sterling scored twice, that England star Sterling had been kicked and had racial slurs directed towards him in an altercation outside the club's training base
GMP were made aware of an incident, which is being treated as a hate crime, on Clayton Lane on Monday and arrested a 29-year-old man on suspicion of racially aggravated assault the following day.
Detective chief inspector Paul Walker said: "Earlier this morning we arrested a 29-year-old man after investigating a racially aggravated assault in Manchester.
"Racism will not be tolerated in Greater Manchester and has no place in civilised society."
City have not issued a statement relating to the incident.