The 33-year-old is said to have rebuffed to travel with the club because he thinks his future with the London-based club remains uncertain.
After rejecting to follow the team to the US, Arsenal released a statement stressing how disappointed they are with the centre-back’s decision.
"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."
Following his unsure career at the club, the former France defender has been linked with a move back to the Ligue 1 with Lyon and Bordeaux considered as the potential suitors for his services as well as German giants Borussia Dortmund.
Arsenal will begin their pre-season campaign with a friendly against Colorado Rapids in Denver and three International Champions Cup games.
After returning from a long-term Achilles injury in December the captain for the side featured just 17 times for the Gunners in the 2018/19 Premier League season and ten games in the Europa League.
Arsenal recruited Koscielny for a fee said to be in the region of £8.45 million from Ligue 1 outfit Lorient in 2010.
