The centre-back is under contract at the Britannia Stadium until the summer of 2014, but reports have suggested that he could join Tottenham.
Speculation has implied that Shawcross is one of Spurs boss Harry Redknapp's top targets after missing out of Blackburn's Phil Jones.
It has been rumoured that Wilson Palacios could be offered as part of a deal to entice Stoke to part with Shawcross.
But Coates told The Sentinel: "We see Ryan's future at Stoke City. He is a very good young player and I expect him to be at Stoke next season.
"I think with Ryan and Robert Huth we have two of the best centre-backs in the Premier League, and we don't want to change that."
Shawcross was an unused member of England's squad in the 2010 friendly with Egypt, but has not been selected again by Fabio Capello since that time.
Source: Team Talk
Source: Team Talk