Last week, it was reported that Liverpool could be close to signing the Bosnian international should Pepe Reina leave Anfield this summer.
However, Coates, who appointed Mark Hughes as manager at Stoke City on Thursday to replace Tony Pulis, says Begovic is thought of very highly at the club.
“But he is also ambitious. If top clubs come for your players, I do not think you can deny them the opportunity. That is my view.
“But it would depend very much on the money being right. We are not looking to sell him. We are not expecting to sell him. We expect him to be our goalkeeper next season.”