The 21-year-old has impressed with his performances for the Gunners this season and talks of a move out of the club - possibly to the Nou Camp - have surfaced.
Although he initially laughed off links to the European champions on his Twitter account by saying: "Please continue the 'Szczesny to Barcelona' rumours. Makes me laugh everytime I read it. Haha.", he has now opened the doors to join them.
He was quoted as saying by polskathetimes.pl: "I can't declare that I will spend my entire career here, but if I leave I will have a very important reason or I will go to Barcelona.
"I can't imagine a situation where I would leave this club just for money."
The Polish international has also been embroiled over his comments made over the Arsenal captaincy.
He said via Twitter: "I got annoyed with a few things about myself in the media recently so I'm going to set the record straight.
"I never said I deserve [the] Arsenal armband. I said that I would love to one day take [the] responsibilty of being an Arsenal skipper.
"Robin van Persie is doing a great job as a skipper and he fully deserves [the] armband.
"I am injured and had to be pulled out of Polish national team. Hope to recover as soon as possible. (That's for Polish media.)