According to journalist John Cross from Mirror, Koscielny is unhappy at Arsenal and has a big offer from France.
Arsenal just confirmed that their captain refuses to travel to US for summer tour.
Bordeaux are believed to have offered the defender a three-year deal to bring him back to his home nation.
Fellow Ligue 1 sides Lyon and Rennes have also shown an interest but it leaves Koscielny, 33, in a difficult position as Arsenal have been in no rush to discuss new terms.
Koscielny only has 12 months left on his existing contract at Arsenal.
There is a feeling that Arsenal will just allow Koscielny to run down his contract but the captain is looking for longer term security.
Bordeaux’s offer is believed to be two years with a third year option and they hope a fresh challenge could appeal to the veteran centre-back.