Northumbria Police confirmed they had received a complaint in the wake of City's 3-1 Premier League victory at Newcastle.
A spokesman said: "Northumbria Police has received a report of racist language having been used at the St James' Park stadium during the Newcastle United v Manchester City match.
"Northumbria Police takes such allegations extremely seriously and enquiries are ongoing into the incident."
It is understood 27-year-old Serbia international Kolarov became involved in a lengthy exchange with a supporter carrying an Albania flag as he warmed up on the sideline during the game.
There is a long history of tension between Serbia and Albania, particularly over the disputed Kosovo region.
Neither club was commenting on the matter, although it is understood Kolarov will be spoken to by police next week.
The defender was introduced as a 37th-minute replacement for the injured Samir Nasri but was also substituted 18 minutes from time.
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