The Poland goalkeeper signed a new long-term deal at the Emirates last November and is firmly established as the No.1 in Arsene Wenger's side.
Arsenal have been linked with moves for the likes of Real Madrid's Iker Casillas and Barcelona's Victor Valdes this summer, but Szczesny says he would be happy to battle anyone for a starting spot at Arsenal.
"If they give me a contract to the end of my career, I'd sign it without any hesitation," Szczesny told Polish newspaper Przeglad Sportowy.
"I feel attached to the club and the coach who has given me a chance.
"There are not many who would do that but I must have been good. I see the future here.
"I'll play at Arsenal as long as am wanted here. I am not afraid to fight for number one with anyone: Fabianski or Casillas.
"I hope I won't make the boss think, 'Wojciech's not number one'. It's all in my hands. I am in the best form of my life."