Although Shawcross' current contract does not expire until the summer of 2014, the 25-year-old's recent progression into the England ranks has put him in the shop window.
It is why Shawcross is understood to have been offered a new six-year deal to ward off any predators, notably Manchester United manager Sir Alex Ferguson, and Pulis said: "We're hoping and praying Ryan will be a Stoke player for the rest of his life."
"But if a top-three, top-four club came in, and they paid the money, there is no way in a million years we would be able to prevent Ryan from going."
He added: "If we do a deal there will be no one more pleased than myself. We took Ryan as a young lad and he has grown with the football club, he has been fantastic for us, and the club has been fantastic for him as well."
Shawcross joined Stoke from United in 2008 for £1million at a time when Ferguson's squad was heavy on defenders. But in his programme notes for last month's game with Stoke, Ferguson suggested he had made the wrong decision in letting Shawcross go.
Pulis is further hoping a deal can be done before Shawcross' current contract enters its final year.
"We would hope that's not the case, especially with Ryan, which is why we're talking to him now, to get it done," added Pulis.
"You hope it gets sorted out nice and quickly, but we recognise and realise there is still a lot of time for it to be done, not just weeks and months.
"But then he has to do the best he possibly can for himself and his family. He has two lovely little kiddies and he has to look after them, and that's important."