The 25-year-old moved to the Britannia Stadium last year from Werder Bremen, but has ambitions to move to a higher level.
"I've had a year at Stoke and I've had one good season," The Sentinel quotes Arnautovic as saying. "Now I want to have another good season.
"As long as I'm at Stoke, I'll be at full throttle for the team. Whether I move on after this season or after the third or after the fourth, no one knows, only God knows."
Arnautovic, who had a loan spell at Inter Milan in 2009 while he was an FC Twente player, is tied down to Stoke until 2017.