The England forward was believed to have been kicked and branded a "n--" by a man who appeared to be waiting for the 23-year-old at the players' entrance at City's football academy training base, according to sources.
When Sterling got out of his auto, the man is alleged to have kicked him and shouted racist abuse.
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A man has been arrested over allegations of a hate crime against a player for the English soccer club, Manchester City, at the club's training ground, police said on Tuesday.
The newspaper said it is understood that Sterling got out of his vehicle to ask what the problem was but was then kicked in the leg. He is now in police custody for questioning.
Greater Manchester Police have been investigating the incident and are treating it as a hate crime.
The Sunday Telegraph newspaper reported that Sterling was apparently kicked and racially abused as he arrived at City's Etihad Campus on Saturday morning before their 4-1 win over Tottenham, during which the attacker scored twice. Pep Guardiola's side are now 11 points clear of Manchester United at the top of the Premier League and have won their last 16 top-flight matches in a row.