The 33-year-old refused to travel with the Gunners when they departed for the US on Thursday.
His actions were condemned by the club, who released a statement, saying: "We are very disappointed by Laurent's actions, which are against our clear instructions.
"Laurent Koscielny has refused to travel to the US for our pre-season tour. We hope to resolve this matter and will not be providing any further comment at this time."
Metro says Koscileny is weighing whether to pay the remaining amount of his £90,000 per week contract, which is set to expire in June.