Faye, a £2.25m signing from Newcastle in August, only missed two games in the Potters debut Premier League season.
"I'm very proud because I have so many trophies, I don't believe it," he told BBC Radio Stoke.
The 31-year-old added: "I would love to stay (for the rest of my career). I'm very happy here and I have everything. The supporters love me, and the manager is very good. I hope to stay here because I love Stoke City."