The 29-year-old Pole, who played in Saturday's FA Cup final win over Hull City, is due to be out of contract in the coming weeks.
Despite revealing that he is likely to join another club next season, Fabianski is happy with how his last game for the Gunners turned out.
"It was probably my last game for Arsenal," he is quoted as saying by Sky Sports News. "I don't know what I can say, but if I end my Arsenal career in that way then it is the best way to finish."
Fabianski joined Arsenal from Legia Warsaw in 2007.