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.
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"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."