The 32-year-old's current deal expires next summer but he wants to extend his stay and hopes his performances this season will be enough to persuade manager Tony Pulis to do so.
"This is the last season of my contract, but I would prefer to stay here," he said. "I am happy here, the fans like me and I have everything here.
"Maybe I have three years left before I finish football, but I am happy here, so why go somewhere else?"
Faye has been a key figure in keeping Stoke in the top flight for the last two years, having joined just prior to their maiden Premier League campaign.
He has enjoyed the experienced immensely and believes the team is probably the strongest it has been since coming up from the Championship.
"When I first came to Stoke some people said the club was going straight back down, but I said I wanted to come here and I wanted the challenge," he told The Sentinel. But we stayed up then and in the second season as well. Now this year we have a strong team and more good players.
"Everyone works hard together and enjoys the game. The team spirit is as good as it was."