According to L'Equipe (via The Mirror), representatives from the two clubs met in London this week.
Koscielny infamously decided against joining the Arsenal squad on their pre-season tour of the US.
Bordeaux will reportedly try to persuade Arsenal to release Koscielny, but Arsenal are not expected to budge from their £9m valuation.
The Ligue 1 outfit's president Eduardo Macia has spoken publicly about wanting Koscielny.
"If there's a chance, we would be thrilled to have him [Koscielny] come here.
"He's a leader, an intelligent defender and one of the best defenders whom I've seen in my career.
"It would be incredible to have a player of his quality at Bordeaux. But he has a contract at Arsenal."
However, Arsenal are reportedly seeking to sign a centre-back themselves, and if they fail to do so, they may force Koscielny to stay and see out his contract.
