The centre-back has reportedly had lucrative offers from France but the Gunners want to let his contract, which expires next year, run down.
Laurent Koscielny has refused to travel for Arsenal's pre-season tour of the USA, the Gunners have confirmed.
The Frenchman is the north London club's captain but they are reportedly open to offers for him this summer as Unai Emery looks to reshape his defence.
Koscielny has been a long-term servant at Arsenal having first joined them in 2010.
He missed the first half of last season with a serious achilles injury that ruled him out for 10 months, a duration that included the 2018 World Cup which his nation France went on to win.
A club statement on Thursday morning read: "Laurent Koscielny has refused to travel to the US for our pre-season tour.
"We are very disappointed by Laurent’s actions, which are against our clear instructions.
"We hope to resolve this matter and will not be providing any further comment at this time."
Arsenal are reportedly ready to let Koscielny's contract, which expires in 12 months time, run down.
A return to France for the centre-back has been widely mooted, the 33-year-old having previously played for Lorient, Tours and Guinamp in his homeland.
Bundesliga side Bayer Leverkusen are also said to be interested in signing him.
But a number of big-money offers from Ligue 1 have apparently turned the Frenchman's head.
Bordeaux are beleived to want to sign him on a three-year contract, and 33-year-old Koscielny keen on securing long-term security.
Arsenal are set to announce the signing of 18-year-old Saint-Etienne centre-back William Saliba for £26.5 million, having fought off competition from north London rivals Tottenham for his signature.
Saliba's arrival would likely see Koscielny move further down the defensive peckin order at the Emirates and he is keen to get regular first-team action in the latter years of his career.
The Gunners are also persuing Celtic left-back Kieran Tierney, having submitted a £15m bid for the defender already, but the Hoops value him at £25m.
And new technical director Edu, who will oversee recruitment as part of his new role, will have a say on any future investments, with Crystal Palace forward Wilfried Zaha another key target this summer.