The Gunners captain sat out their trip Stateside on Thursday as the 33-year-old defender looks to orchestrate a move this summer.
Koscielny is thought to have to asked Arsenal to allow him to end his contract a year early to secure a return to France.
Reports in England suggest that the experienced Gunners skipper is attracting interest from Bordeaux, Lyon and Rennes.
Former Arsenal striker Wright questioned Koscielny’s “love and loyalty” for the Gunners after his decision to sit out the tour.
“For our captain who has been there for nearly 10 years, to get to a station where he is giving us unbelievable service. We’ve seen him play through the pain, build a legacy and a legendary status he deserves,” Wright said on his YouTube channel.
“I have to question Laurent’s loyalty and love for the club to do this in pre-season, when you are the captain with young players, a time in the season when everyone should be together.
“This is going to be a tough season for Arsenal because we are in transition and we have a lot catching up to do. For our captain to refuse to go on a pre-season tour after nine years of unbelievable service to destroy your legacy at a club that you’ve to professed to love it’s baffling.
“Why? Who are you advisors? What are they saying to you? Your’e the one who has built up this legacy which is why the fans love you so much. You’re our captain, you’re our leader.”
Wright added: “We don’t need this right now at Arsenal, we are behind the eight ball. We don’t need our leaders coming out doing things like this. It doesn’t set a good example to the numbers.
“I love you Laurent but this is a poor decision to make.”
Koscielny moved to Arsenal from Ligue 1 side Lorient in the 2010 summer transfer window.
The France international has netted 27 times in 353 games in all competitions over the past nine years at the north London side.
Koscielny has won two FA Cup titles during his Arsenal career, while the Frenchman has finished as a runner-up in the Europa League and the League Cup.
Arsenal finished in fifth place in the Premier League table last term before Unai Emery’s side lost 4-1 to bitter rivals Chelsea FC in the Europa League final in Baku at the end of May.
The Gunners have only signed Gabriel Martinelli from Brazilian club Ituano so far this summer.
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