Szczesny expects that he will be between the posts this weekend against Newcastle United, but accepts that he will have to perform well to keep hold of the gloves.
"I received a clear signal from Arsene Wenger before the new season that I would be the number one keeper in the Arsenal goal," revealed Szczesny.
"The other keepers in the team must compete with me, but I do not plan to give up.
"Of course, I feel under pressure. I know very well how good a keeper Lukasz Fabianski is and I must be in top form all the time."
Szczesny joined Arsenal in 2005 from Legia Warszawa.