Fabianski joined the Gunners five years ago but injuries and some high-profile errors gave Wojciech Szczesny the opportunity to take over.
Fabianski told Polish paper Gazeta Wyborcza: "I hope that my adventure with Arsenal has come to an end.
"I intend to leave and play in a strong league. I wanted to leave in the winter, too, but Arsene Wenger did not give a green light."
Fabianski, who has 20 caps, was named the Polish league's top keeper in 2006 and 2007 during his time with Legia Warsaw.