The midfielder has spent this season on-loan in the Championship with Swansea City, where he has impressed.
The London Evening Standard says Patino cannot see a path for himself to Arsenal's first team and instead is prepared to ask for a transfer this summer.
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And Gunners manager Mikel Arteta is expected to sanction the sale.
A move to Spain has been mooted for Patino, who holds a Spanish passport and has family connections to the country.