The England Under-21 centre-back has been linked with former club Manchester United, Liverpool and Arsenal in the last few months and is tipped to progress to the senior national side at some point. Stoke have opened talks on a new four-year contract and Coates said the club are determined to hang on to their best players.
"He's a big asset to us and is a very promising young player but he needs to keep his feet on the ground and not get carried away," the chairman told The Sentinel. "He's got a lot of hard work to do and I think our coaching staff deserve credit for the way they have developed him."
He added: "But he also deserves praise because he is dedicated to what he does.
"We always try to look after contracts. Players are valuable assets, so it is important to make sure you look after the contracts.
"Ryan is a good example of that."