The 25-year-old has become an integral part of the Potters' team since his move to the club from Manchester United five years ago, and Pulis is delighted with how the defender has progressed as a player.
"We are very close to doing a deal with Ryan," Pulis said 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.
Pulis has also praised Shawcross’ attitude following his on-field battle with Everton’s Marouane Fellaini on Saturday during the 1-1 draw.
The scrap resulted in the Belgian midfielder headbutting Shawcross and his manager praised the England international’s temperament following the incident.
"It takes a lot to keep calm in those circumstances,” Pulis continued. "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."