The 25-year-old's current deal expires in 2014 and it is understood that a host of Premier League clubs are monitoring proceedings. However, Coates has remained firm on the player's future.
"Ryan is an important player for us. And we want to keep him and make him secure. You try to look after your assets," Coates told The Sentinel.
"He has developed his career at this football club and we want him to stay, so it's up to us to find a way of keeping him."
Shawcross joined Stoke from Manchester United in 2008.