Manager Tony Pulis confirmed talks are at an advanced stage with the 22-year-old central defender and hoped an agreement would be sealed within the next few days.
"I have had long discussions with Ryan over his future and I am delighted that he sees his future here," Pulis told the club's official website. "There has been a lot of speculation surrounding Ryan, but we have made it quite clear that he is going nowhere and we are delighted to be in a position now where we can secure his future."
He added: "He is an exceptionally talented young lad who had an important part to play at this football club, so I am confident that he will be a major influence upon what we are aiming to achieve."
Shawcross, who has been capped at England Under-21 level, completed a permanent move from Manchester United to the Britannia Stadium in January 2008 after an impressive six-month loan spell.
"I am very happy at Stoke and I always saw myself being here for some time to come, so I am delighted we are very close to coming to an agreement," said Shawcross.
"The fact that discussions have gone so well with the manager means I have given the green light to my agent to have further discussions on a new deal."