A 24-year-old is in custody on suspicion of a racially aggravated public order offence, Wiltshire Police said on Saturday.
Cole, who played left-back for Arsenal and Chelsea during a lengthy top-flight career, was part of the ITV broadcast team when Swindon Town played Manchester City at the County Ground earlier this month.
The incident reportedly occurred in the corner between the Town End and the Don Rogers stand, where the ITV punditry team was based.
Superintendent Phil Staynings, Swindon commander, said: “Racial abuse of any kind will never be tolerated by Wiltshire Police.
“We have worked closely with the football club, who share our strong stance on this, and would like to thank them for their support in our ongoing investigation.
“We continue to encourage people to report these types of incidents and I’m pleased that my officers have been relentless in securing this positive arrest.
“We will continue to work with the club to stamp out hate crime of any kind that spoils matches for the majority of supporters.”
Premier League champions City eased past League Two Swindon 4-1 during the match on January 7.
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