Olic claimed last month that Stoke had made him an offer to join this summer and City boss Mark Hughes confirmed his interest in the experienced marksman.
Now the 34-year-old, who is out of contract with German club Wolfsburg at the end of the season, has confirmed that he is hopeful of finalising a move to the Britannia Stadium.
The former Bayern Munich man has been linked with big-money moves to America and Asia, but he says a chance to play in the Premier League is too good to turn down, although he added that no deal has yet been agreed with Stoke.
"There are many rumours about my future. The press are talking about me moving to United States, to Qatar, but Stoke City remains my first choice," he confirmed to Jutarnji List.
"They are very serious and it would be really nice to play against Manchester United, Liverpool and other great English clubs.
"But nothing is signed yet so anything can happen. I also have some offers from Germany, even my former club Hamburg wants me. Never say never, right now the only thing I can say is that I will make my decision this month."