Middlesbrough manager Gareth Southgate has admitted he would love to retain striker Tuncay but expects him to move on before the end of the month.
Tuncay, 27, is available for Saturday's trip to Swansea but Southgate fears it could be one of the final appearances for the Turkey forward in a Boro shirt.
"We haven't had any bids for him but while we have him, I want to make the best use of him," he told BBC Tees.
"Unfortunately we don't expect to have Tuncay beyond the end of this month."
The striker has become a huge favourite with supporters after a free-transfer switch from Turkish club Fenerbahce in June 2007, making 67 league appearances and scoring 15 goals.
One player who has been linked with a concrete move away from the Riverside is striker Afonso Alves, and Southgate remains hopeful of a breakthrough in the deal.
Alves, 28, became Boro's record signing when he joined from Dutch side Heerenveen for £12m in January 2008, but has struggled to make an impact.
"We agreed a fee with a club in Qatar and his representatives are talking to another club at the moment but we haven't agreed a fee with that club," Southgate told BBC Tees.
"We're expecting that things may move on in the next few days.
"I expect there to be movement and when players go out I'd like to strengthen what we have, but it's quite frustrating at the moment."
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