An incident is alleged to have occurred during the first half of City's 3-1 Premier League win, as Kolarov warmed up on the touchline.
Kolarov became involved in a lengthy exchange with the supporters, who are understood to have waved an Albanian flag near the Serbia international.
The pair are believed to have complained to stewards, who then alerted police.
Northumbria Police confirmed they had received a complaint in a short statement that read: "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."
There is a long history of tension between Serbia and Albania, particularly over the disputed Kosovo region.
Kolarov was introduced as a 37th-minute replacement for the injured Samir Nasri, but was substituted himself 18 minutes from time.
Neither club has yet commented on the matter.
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