Shawcross, who has 18 months to run of his current deal, has been linked with a move to Manchester United, Liverpool and QPR.
He has been offered a bumper six-year contract to stay at the Britannia Stadium and he suggested after Saturday's win at West Brom that he would stay with the Potters.
Pulis said: "I don't think (Shawcross' contract) is going to be too much of a problem."
Asked if it would be signed by Christmas, he added: "It will be done before then, I think.
"The issue is keeping his feet on the ground and keeping him level-headed. But he doesn't seem to be the sort of character to get carried away.
"If he does, he will be told. It's a big contract for Ryan and a big deal for the club as well.
"We have to make sure both parties are happy about it and there are little things we have to iron out. It's not far away.
"If you look at our club we have four outstanding young players in (Asmir) Begovic, Marc Wilson, (Steven) Nzonzi and Ryan. We certainly want Ryan to be part of that group which will grow with the club."
Shawcross said: "Talks are ongoing. I'm happy, the club are happy. It's just one of those things, these contracts take time.
"I've told them I want to stay. Ultimately, it's up to my agent and the club to sort it out. I haven't got too involved, I've left them to it. When it's sorted, we'll tell you."