The defender is ready to exit the Emirates Stadium this summer unless the Gunners are ready to show the ambition to fight for their first piece of silverware in over eight years.
Arsene Wenger's side last won a trophy over eight years ago - the FA Cup in 2005 - a spell that has seen the club sell a string of top players like Cesc Fabregas, Samir Nasri and Robin van Persie, often to league rivals.
Now the 27-year-old, who has been linked with a move to Bayern Munich, hopes the north London outfit is ready to prove its ambition in the league next season, otherwise he will look for a new challenge elsewhere.
"I feel good at Arsenal, if we have ambition to fight against the other teams of course I want to stay here," Koscielny told Eurosport. "It's hard psychologically. We are constantly pressured because if Arsenal is not in the Champions League it would be a catastrophe.
"I have to see if I have clubs interested in me. I will not go to any club. I want to maybe discover another league. Paris [Saint-Germain]? There has been no contact yet. It is hard to not win titles year after year. We are competitors, professionals, we want to win. I want to add to my list of achievements. If Arsenal cannot allow me that, I'll seek a move elsewhere."