The Athletic reports the Gunners will move to extend the Swiss star's five-year stay at the Emirates as they have not received a bid matching their valuation.
Arsenal were open to selling the midfielder after his solid showing at Euro 2020 for Switzerland.
But having weighed up the cost of replacing the 28-year-old against the on and off-field qualities he brings to the club, Emirates chiefs have reportedly decided against letting him go.
Roma have already had a £13million bid rejected by the Gunners. Xhaka is contracted until 2023.
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