This was confirmed by the club in a terse statement on Thursday morning.
It 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 & will not be providing any further comment at this time.”
It is believed that the 34-year-old defender wants the club to cancel his contract, so he can consider offers to return to France.
Koscielny has been with the Gunners for nine years.