The Austria international striker has struggled to make an impact since signing for Inter in August.
Arnautovic's legal representative Peter Baars told TMW: "Marko is owned by Twente and on loan at Inter.
"If the Nerazzurri don't want to sign him again he will return to Holland. It's a possibility. If there are teams interested they can deal with Twente. He has now grown up and is worthy of playing for a big club.
"Twente are doing very well, so eventually he might not leave. Actually, if he doesn't find another team it would be something he would welcome."
When asked if there is any chance Arnautovic might stay at Inter, Baars said: "Yes, there is a fixed price to buy him. If they want, Inter can sign him.
"He is a valuable player. I imagine there would be other Italian teams interested because he has great qualities.
"Anyway, if no one wants him, he'll return to Twente."