The long-term contract, which would keep him at the club into his 30s, is understood to be very close to being signed, with confirmation expected in the next day or two.
Shawcross, 25, joined Stoke from Manchester United, initially on loan, in 2007 and has become one of the Potters' most valuable assets, making his England debut against Sweden this month and attracting reported interest from a number of Premier League clubs.
The defender hinted he is ready to put pen to paper following Stoke's 1-0 victory over Fulham on Saturday, telling newspaper reporters: "I am very happy here and very settled here.
"I have loved my five years here so far and I want that to continue. We have progressed incredibly from when I first came. The people here have looked after me really well, the fans have been brilliant with me and I want to be a part of the future."
Stoke boss Tony Pulis has consistently pushed Shawcross's England claims, and he has no doubt the Chester-born player deserves the long-term deal.
"Ryan has been immense for us," said Pulis. "I took him from Manchester United's third team and I remember him scoring on his debut at Cardiff - and he's improved ever since.
"Ryan has done brilliantly for us, but the club has also done brilliantly for him as well.
"We are more than happy to give Ryan that length of contract. He is loved to death by everyone here and he's such a big softie at times because he's such a big family man."