The wing-back is set to move to Serie A champions Napoli for a fee of €20m, says Sky Italia.
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Only a few final details remain to be ironed out with the player, who has already given his approval to the move to Naples.
TMW says Gutierrez will pen a contract worth €2m net per season.
Once his deal is finalised, Napoli chief Giovanni Manna's next move will also be Spanish, with Sevilla fullback Juanlu Sanchez a firm target.