The 22-year-old Poland international has seen Lukasz Fabianski impress in keeping two clean sheets in Arsenal's last two games - but has reiterated his loyalty to the Gunners.
Szczesny said: "I am too happy to go somewhere else. I believe in the philosophy of the club and that Arsenal will start to win again.
"I have a debt to pay here for the club, I owe them. I just do not want to go anywhere else. As long as they want me here, there is no 'somewhere else', and I have a contract until June 2015."
On Arsenal's poor campaign, he added: "It is halfway through March and we have lost everything. There are still 10 matches left to save the club against the humiliation of all times.
"It would be disaster not to be in the top four and without Champions League next year. We have the 10 most important games in our careers. We are going through the most difficult time since I came here."