Koscielny's future at Arsenal is reportedly in doubt after entering the final year of his contract with no sign of a new deal.
The 33-year-old has been linked with a return to France with Bordeaux.
Arsenal confirmed the news in a statement that said: "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, who joined Arsenal from French side Lorient in 2010, has made over 350 appearances for the club. He last signed a contract extension in 2017, with that deal expiring at the end of the 2019-20 campaign.
The centre-back suffered a serious knee injury against Atletico Madrid in May 2018, ruling him out of France's victorious World Cup winning campaign that summer, before he returned to action last December.
Arsenal will face Colorado Rapids in a friendly on July 16 before taking on Bayern Munich, Fiorentina and Real Madrid in the International Champions Cup. They kick off their Premier League campaign at Newcastle on Aug. 11.
Meanwhile, Arsenal have condemned "unacceptable racial abuse" suffered by 20-year-old Jordi Osei-Tutu, who is on loan from the north London club at German side VfL Bochum.
Bochum were playing Swiss team St Gallen on Tuesday evening when Osei-Tutu left the field in tears after an interaction with an opposition player.
In a statement released shortly after the incident, Arsenal said: "We are working closely with Bochum and Jordi and we are giving him our full support. Racism has no place in our game and we do not tolerate any form of discrimination."