The Frenchman left his homeland in 2010 when he joined the Gunners from Lorient.
The centre-back has since made 353 appearances for Arsenal, winning back-to-back FA Cups in 2014 and 2015.
However, his future is now in doubt with Bordeaux making his signing a priority this summer.
Manager Paulo Sousa wants to add some experience to his backline after last term’s bottom-half finish.
Koscielny is said to be interested in Bordeaux’s project and could ask Arsenal to leave a year before his contract expires.
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