The Gunners have been linked with the Holland international in recent weeks.
And Spain's ABC reports Arsenal have approached Barca this week to discuss a fee for Depay.
While he joined Barca last summer from Olympique Lyon, Depay only penned terms to 2023, so leaving Barca with the prospect of either selling him or handing the striker a new deal.
Arsenal's initial approach involved asking Barca to name their price for Depay.
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