Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The Polish goalkeeper was left out of the Gunners squad for their Champions League trip to Bayern Munich and remained on the sidelines for a 2-0 Premier League victory over Swansea.
Reports claim that Arsene Wenger has lost faith in the 22-year-old and will look to bring in a new shot-stopper over the summer.
That could force Szczesny through the exits, as he goes in search of regular first-team football elsewhere.
He is, however, adamant that he has no intention of securing a switch, with there a desire on his part to be a mainstay in the Arsenal side for many years to come.
Szczesny told Gazeta Wyborcza: "Physically, I can imagine myself at a different club, yes, but mentally, absolutely no. I'm too happy here.
"What guarantee do I have that I will win trophies somewhere else? Arsenal will win things again, I trust the club's philosophy, I have a debt here.
"I don't want to be anywhere else. My contract runs out in 2015. I have played my 100th game for Arsenal and I hope to play hundreds more."
Szczesny concedes that the 2012/13 campaign has been tough for everyone at Arsenal, but he hopes both he and the club can end a frustrating season on a high.
He added: "I know that Arsenal should not play as badly. We're not even through March and we have lost everything. We have only nine games to save the club and not humiliate ourselves.
"Arsenal have been in the Champions League for the past 16 years and it would be horrible not to qualify this time.
"Those are our most important games in our careers. It's our hardest time since I got here."