The Telegraph claim the incident occurred last night when the 24-year-old was seeing off a friend at Heathrow Terminal 5.
Xhaka's friend was refused entry on to a flight to Germany after arriving late for boarding, and a witness claims the Switzerland international then racially abused a member of staff in German.
Airport security and police were called before the midfielder was taken to a west London police station for questioning.
Arsenal star Granit Xhaka has been accused of racial abuse after an incident at Heathrow Airport
A Metropolitan Police statement read: “Police were called at 19:29hrs on Monday, 23 January following an allegation that a member of staff had been racially abused at Heathrow Airport, Terminal Five.
“The allegation was made by a third party. Officers attended and spoke with a man in his 20s.
"He was not arrested. He voluntarily attended a west London police station where he was interviewed under caution.
Arsenal 2-1 Burnley: 10 key stats
Sun, January 22, 2017
Express Sport brings you 10 defining statistics from Arsenal's victory over Burnley at the Emirates
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Express Sport brings you 10 key stats from Arsenal's win over Burnley
Arsenal star Granit Xhaka received his second red card of the season against Burnley
Arsenal have refused to comment on the issue, stressing it was both a private and police matter.
Xhaka, who joined Arsenal for £34million from Borussia Monchengladbach last summer, is already in hot water after receiving his second red card of the season in Sunday's 2-1 win over Burnley.
The midfielder is facing a four game ban and is set for showdown talks with Arsenal boss Arsene Wenger this week.