Yilmaz only joined the Turkish champions from Trabzonspor last year but is attracting interest from Europe's biggest clubs after scoring eight goals so far in this season's Champions League.
Terim acknowledges the interest and likens Yilmaz to Andriy Shevchenko who he worked with when he took the reins at AC Milan in 2001.
"It's not going to be easy to keep him," said Terim, quoted in The Observer.
"He has targets but it will be his decision. Being wanted is a good thing, but we are fond of him and believe he will do great things for us in the future.
"He listens. He is 27 but he is still open to learning new things. Burak senses goals. He can score any time and from anywhere. I'm really fond of him, he has been a miracle signing.
"Andriy Shevchenko was the same. If you substituted him in the 89th minute he would be angry. Burak is the same. He is always thinking about scoring one more goal.
"Loving football is very important. I think he is going to get better and better."