The 23-year-old has been linked with both Liverpool and Tottenham but says he is happy to remain with the Potters.
"I suppose if you are linked with clubs it shows you are doing well," Shawcross told the Sentinel. "But I am a Stoke player, I have signed a contract here and I am happy here.
"The chairman has said the club aren't going to sell me. I don't want to leave and I am looking forward to the new season.
"Any young player in the Premier League is going to have speculation written about him, but it doesn't bother me."