The 54-year-old has been in charge at the Britannia Stadium since June 2006, when he rejoined the club following Peter Coates's takeover.
When asked whether he harbored aspirations of managing a bigger club one day, Pulis responded: "The most important thing for me is this football club.
"I've been here nearly 10 years now, over two spells, and I've still got the desire and hunger to push this football club on. Personally, I don't think there's many football clubs that I'd want to go to if and when my time comes at Stoke. I still have a lot of work to do here and have still got ambition.
"I still wake up every morning desperate to come in and put things in place that will improve the football club over – hopefully - the next 10 years."
The Potters are currently 13th in the Premier League table, having taken eight points from their opening eight fixtures.