As exclusively revealed by Goal in April, the Gunners made an enquiry over the £4.3 million-rated right-back, who was seen as the ideal replacement for the seemingly outgoing Bacary Sagna.
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"We have made an offer to Sochaux: deadline Monday. There is also another player we're tracking just in case," he wrote.
With the deadline arriving, Corchia's agent, Francois Gilles, indicated that the right-back's decision is to join Lyon.
"Sebastien has chosen," he told reporters. "Lyon is the future, this is what he wants [and] is what he has planned. I can at least confirm that today."
Corchia has made 67 appearances for Sochaux since his move from Le Mans in 2011 and has a combined total of 50 appearances across all youth levels as a France international, up to the Under-21s side.