The French right-back was linked with the Gunners during the summer transfer window, but stayed at Sochaux as the deadline passed.
The 23-year-old was also tracked by Ligue 1 giants Marseille, and the report claims Elie Baup's side could also return in the winter window with a fresh offer.
They failed to reach an agreement with French international Anthony Reveillere - who is currently a free agent - and may rival Arsenal for Corchia instead.
Speaking to French newspaper L'Equipe, Corchia said: "I know what I have to do now during matches and I will see what happens in the next windows.
"But at the moment, I want to work with my club. [Leaving in the winter] can be a possibility, Sochaux negotiate with interested clubs. I prefer to focus on the present at the moment."
Lyon were also linked with Corchia in the summer, after the talented attacking full-back enjoyed a superb campaign in Montbéliard.
The Arsenal target was a regular for France's under-21 squad but has failed to make an appearance for the senior side yet.
He was linked with the Gunners due to Bacary Sagna's contract situation. The France international has yet to agree terms on a new Arsenal contract, and his current deal expires at the end of the season.
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