Shawcross has been linked with a move away from the Britannia Stadium after reportedly attracting the interest of several of the Premier League's top clubs.
However, he appreciates just how much the Potters have done for his career and does not plan to go anywhere.
"I'm very happy here and very settled here," said the centre-back. "I have loved my five years here so far, and I want that to continue.
"We have progressed incredibly from when I first came here and I want to be part of the future. The people here have looked after me really well and the fans have been brilliant."
Shawcross credits Pulis for helping him develop into the player he is today, having been spotted by the manager during his time as a Manchester United reserve in 2007.
"I wouldn't be where I am now without the help of the gaffer, I am certain of that," he said.
"The gaffer brought me here as an unknown player and then gave me the captaincy at the age of 21.
"So he has shown incredible faith in me, both as a player and as a person. He has undoubtedly been the biggest influence on my career, no doubt about that."