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 new six-year contract and indicated after Saturday's win at West Brom that he has no desire to leave the Potters.
The 25-year-old's displays also paved the way into the England squad this season, making his debut against Sweden in Stockholm last month.
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.
Asked if a deal had been agreed in principle, he said: "No, we're not that far along yet - but the main thing is that I want to stay and they want to keep me. They're the two things that need to happen first of all. Hopefully it will all be sorted."
Shawcross admitted Pulis was the key reason for him to stay with Stoke. He said: "The main reason I want to stay is the gaffer. He's been great to me throughout my time here and made me captain at a young age.
"I've told him I want to stay here. I feel like he's improved me every year and he got me into the England squad because that's been a goal of mine. It showed a Stoke player can get into the England squad because that's been an issue before."
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