The veteran goalkeeper is on a deal to the end of the season.
Originally coaxed out of retirement last season, Szczesny made such an impact that his deal was extended into this campaign.
But he admitted to TV3: "My family and I are very, very happy. We love being here.
"I know I won't be here much longer because I'm getting older, but it's been a fantastic experience for me and my family. We're very grateful for the time we've spent here."
Szczesny also said: "As the second oldest player on the team (he turns 36 on Saturday), I'm proud of what this team has shown in the competition (Champions League) this year, including our performance at the Metropolitano.
"It was incredible."
