Arsenal face a battle to keep hold of the French defender with Bordeaux eyeing his services.
The Ligue 1 outfit have made Koscielny their number one target this summer.
And the 33-year-old is just as keen on a return to his homeland after nine years in north London, reports L’Equipe.
Bordeaux are not short of cash with Jules Kounde on the cusp of a €25m (£22.4m) move to Sevilla.
Dialogue between the player and the French club has been ongoing for several months and Koscielny has told them he is interested in what they have to offer.
Reports in France claim the defender is asking Arsenal to let him leave for nothing, but that is countered by claims that the Gunners want €10m (£9m).
Koscielny made 17 Premier League appearances last season following Unai Emery’s arrival which is his lowest amount since moving from Lorient in 2010.
Arsenal’s defence was their Achilles heel last term and the club are desperate to strengthen in that department before the transfer window closes.
Koscielny’s compatriot William Saliba is being lined up following his performances with Saint-Etienne recently.
Les Verts are prepared to let the teenager leave on the pretence they can have him back on loan for the upcoming season – something the Gunners are reluctant to do.
Arsenal are also closing in on the signing of Celtic full-back Kieran Tierney with the two clubs close to agreeing a fee.
The Scottish side are keen to get value for money for the Scotsman having let the likes of Virgil van Dijk go on the cheap.
Emery though is having to make additions to his squad with a transfer budget of £45m, which is a major hinderance.
He is though looking to raise funds via player sales with reports suggesting he is willing to listen to offers for star man Pierre-Emerick Aubameyang.