Koscielny joined Arsenal from FC Lorient in 2010 for an undisclosed fee.
A number of French clubs like Lyon, Bordeaux and Rennes have been linked with Laurent Koscielny during the past few weeks and some rumours have also claimed that Bordeaux are willing to offer him a three-year deal.
An official statement on the club's website read: "We are very disappointed by Laurent's actions, which are against our clear instructions".
To say that Laurent Koscielny's Arsenal career has been impressive would be an understatement.
"We hope to resolve this matter and will not be providing any future comment at his time".
There is perhaps no obvious standout candidate now at the Emirates Stadium to take over from Koscielny - who has not been formally stripped of the captaincy yet - but Bellerin has some support among the fans.
Arsenal captain Laurent Koscielny has refused to go with the rest of the squad to United States of America for their pre-season tour and the club has made this public via a statement released on the club's official website.
The Premier League season will see the Gunners open with a trip to Newcastle on 11 August.
While Koscielny is not the same player he once was, at 33, he was still putting in good performances previous year. Considering this situation with Koscielny, they may try and keep Saliba for the upcoming season instead.
Koscielny subsequently became club captain under former boss Arsene Wenger.
Arsenal chiefs have been made well aware of Koscielny's desire to leave in the past week, but he is demanding that they release him on a free transfer - something the Gunners will not agree to. Then again, you can not let one player dictate your transfer dealings as they sets a poor precedent.