The Gunners have not lifted a piece of silverware since the 2005 FA Cup which makes the French defender nervous for what lies ahead.
Koscielny has been linked with ParisSaint-Germain and although he is content for the time being, he knows he may have to consider his future if the North London club are incapable of achieving success.
"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."