The 26-year-old has been linked with a £15m switch to Manchester City, which would include a reported loan move for Joe Hart to the Britannia Stadium.
"This latest story was certainly news to me and I suspect it is just a bit of speculation," The Sentinel quotes Coates as saying. "That's my guess, anyway, and we have certainly had no approach.
"It is important we keep him for the rest of the season. It is an important season and he is a key player. He certainly hasn't made any noises."
Begovic signed for Stoke in 2010.