According to Foot Mercato (via Inside Futbo), Lyon are the first side to make the Frenchman a concrete offer.
They are offering Koscielny a two-year deal and the chance to return to his homeland.
Lyon, reportedly, have yet to make a bid for the defender, but it's believed that Arsenal will be willing to make any deal easy for their club captain.
With Unai Emery looking to renovate the defensive line, Koscielny, 33, would be forgiven for wanting to keep playing at a high level elsewhere.
Another French club Rennes and German giants Borussia Dortmund are also thought to be considering moves.
Koscielny has made 255 appearences for Arsenal in 9 years and will no doubt be remembered fondly by Arsenal fans if he decided to leave.
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