The Poland international goalkeeper helped Arsenal to claim their first piece of silverware in nine years at the weekend as they beat Hull City 3-2 in the FA Cup final.
Arsene Wenger had used Fabianski throughout the cup campaign and he stuck with him for the final, and that allowed the 29-year-old to sign off in style.
Now Fabianski is looking to the future as he prepares to leave Arsenal, having spent seven years with the club and with his contract due to expire.
"A little time will pass before the situation becomes clear," said the Pole.
"But I want to play every week and there are clubs that can give me the chance.
"One option is to stay in England, but there are also international opportunities. One thing is certain: I will not be unemployed."