Aston Villa were reported to have had a £12.6m offer rejected for the 19-year-old, who is a wanted talent across Europe.
Kilicsoy has three assists to his name this season and via Sporx, the player's agent spoke on how many top clubs want the young talent despite his loyalties to Besiktas.
"I know that clubs such as Bayern Munich, Manchester City, Arsenal, PSG, Monaco, Bayer Leverkusen, Stuttgart are watching Semih. We received information about this, but it has not reached the offer stage."
However van Bronckhorst spoke about the potential move away and how he is certain the teenager will stay even if some of the world’s biggest teams make an offer for him.
"I don’t want to sell Semih Kilicsoy! Good offers may come during the winter break, but I don’t want to sell him.
"Things are going well at the moment, and big teams want to sign these players. One day, the best time for the club and the player will come and he can be sold. (But) I hope he will serve us for many years."