The defender has been part of the Potters' fabric since his 2008 move from Manchester United, where he spent four years in the club's academy.
As it stands, Shawcross has less than a year left on his current contract, and while a deal has not yet been offered, Stoke chief executive Tony Scholes recently claimed that the club want to extend the defender's stay.
"I've always said I'd stay at Stoke," The Sentinel quotes Shawcross as saying. "I spoke to Tony Scholes at the end of last season and since then we've not spoken again, but I've got another year, there's no massive rush. I'm here for another season so that's where we are at.
"It's up to the club. I have a year left and I can only comment on what I've got. If they want to make it longer then I'll be delighted. I've had a great time so far and I want that to continue. But there's got to be a contract there to me sign."
Shawcross has made 380 appearances for Stoke in all competitions.