Shawcross has been offered a bumper six-year deal to stay at the Britannia Stadium and Pulis has previously expressed his hope that everything will be finalised before Christmas.
An agreement remains on track and Pulis has commended the way the 25-year-old has continued to improve since joining Stoke from Manchester United five years ago.
"We are very close to doing a deal with Ryan," said Pulis after Saturday's 1-1 home draw with Everton.
"If we get it done we will be absolutely delighted. He has grown with the football club.
"He joined us in the promotion year and has got better every year. His performances have been exceptional.
"He leads by example. He is not a 'voice' in lots of respects but he leads by setting an example. For instance, he is always one of the last, if not the last, off the training field."
The centre-half was floored by a Marouane Fellaini butt during the game against Everton and Pulis praised Shawcross for keeping cool during a running battle with the midfielder.
The Stoke boss added: "It takes a lot to keep calm in those circumstances.
"It's not an easy thing to do. I would have liked to have seen what would have happened with other players at a few other clubs.
"But Ryan is a lovely family man, he has got everything in order, he works as hard as anybody I have known.
"He trains properly, he eats well, he is a good, good professional."
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar