Enrique has been in contact with Gunners chief Raul Sanllehi as manager Unai Emery battles to turn results around in London.
However, while interested in the job, Spanish sources insist Enrique has told Sanllehi he won't consider taking the post midseason.
Enrique would prefer to wait until the offseason before taking his next job to give himself the best chance to plan for the new campaign.
The Catalan has been out of football since stepping down as Spain coach earlier this year to be with his daughter before she passed away.
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