Reports had claimed that the Polish international could be tempted to leave the Emirates Stadium for a club that is currently challenging for major titles.
However, the 21-year-old has revealed that he is only concerned with winning medals with the Gunners.
"I can't imagine myself in the next few years' time playing anywhere other than here. In fact, I won't move until we win something," said Szczesny.
"Recently, one of the journalists asked me whether I have bigger ambitions than playing for the third place in the Premier League with Arsenal. God, sure I have! I look at the table and realise that is our maximum this year.
"I want to be part of the team that show fans the bad times are over. I won't leave until we achieve this."
Szczesny joined Arsenal as a trainee in 2006.