The French boss is said to be concerned over Xhaka's discipline after he received his marching orders for the second time this season.
But things have gone from bad to worse for the Switzerland international after he was accused of racism during a heated row at Heathrow Airport on Monday.
Reports suggest Xhaka launched a foul-mouthed attack on a member of British Airways staff after his fiancee's brother was not allowed onto the flight due to missing the check-in deadline.
Arsene Wenger is set to hold crunch talks with Granit Xhaka this week
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A Metropolitan Police statement read: "Police were called at 7:29pm on Monday, 23 January following an allegation that a member of staff had been racially abused at Heathrow Airport, Terminal 5.
"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. Enquiries continue."
Arsenal say it is both a private and police matter.
Granit Xhaka received his marching orders for a poor tackle on Burnley's Steven Defour
Granit Xhaka will miss four games through suspension
And according to the Daily Mail, Wenger will address his concerns with Xhaka in a private meeting at the club's training ground in the coming days.
Wenger is set to remind him of his responsibilities on and off the pitch, with the 24-year-old struggling to hit the ground running in north London following his move from Borussia Monchengladbach in the summer.
Xhaka is suspended for the FA Cup tie at Southampton as well as the Premier League dates with Watford, Chelsea and Hull.