The Turkey international has made just two substitute appearances for Tony Pulis' side in the Premier League this term.
The former Middlesbrough marksman lasted just over an hour in Turkey's shock 1-0 Euro 2012 qualifying defeat to Azerbaijan on Tuesday.
Tuncay, who cost Stoke £5million from Boro, has said he will stay with the club until the New Year before taking stock of his situation.
If by then he is still struggling for first-team opportunities then he will seek to continue his career elsewhere.
"I will stay to January and try to get myself into the team," is quoted in the Daily Mirror. "But if I cannot, then I will ask the club to let me go. I have to think about my career and about Turkey."