The £15million-rated Bosnia and Herzegovina international has been linked with Liverpool and Chelsea over recent months after a fantastic season.
But while Coates admits he would not deny Begovic a dream move, Stoke, who appointed Mark Hughes as their new manager on Thursday, would not be prepared to sell on the cheap if at all.
"Asmir is a super professional player," Coates told Sky Sports. "We like him very much. He is a top, top goalkeeper. I think he is as good as anybody in the Premier League.
"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."