Fabianski impressed in last week's FA Cup success against Liverpool.
The 28-year-old's contract expires at the end of the season and he has so far rejected an extension as he wants more regular first-team football. Wenger said: "Of course, it is a possibility that it is his last campaign with us. He wants to play somewhere. But if he changes his mind, my door is open."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball