The Stoke captain has 18-months left on his current contract and the club have offered him a new six-year deal.
"I am happy at Stoke, I have 18-months left and we are in talks but these things take time," he told Sky Sports News.
"I want to stay. I have enjoyed my time here and I am captain, but these contracts take time and there are little things to iron out."
"It is [flattering] but most of it is paper talk, when you have 18-months left you're going to get linked but ultimately I am happy at Stoke and it is just up to my agent and Stoke to sort out."
Shawcross also hoped he can win more England international honours.
"It was great for me and my family, the result was the main thing and that was disappointing and towards the end we crumbled a bit but I was pleased to make my debut and hopefully I will get some more caps."