The 33-year-old has been linked with a return to France this summer with the likes of Lyon, Bordeaux and Rennes showing interest.
Reports suggest that the experienced stopper asked to be released from his contract this summer, only for the club to refuse.
And the experienced centre-back has now taken matters into his own hands after angering his employers by refusing to join the Gunners' squad on the plane.
An Arsenal statement 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.”
Koscielny is in the final year of his contract at the Emirates and made just 17 Premier League appearances during an injury-hit 2018/19 campaign.
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