Gundogan wants to spend the rest of his playing days at the Etihad.
The 30-year old midfielder is enjoying his best spell at Man City under Guardiola since his arrival from Borussia Dortmund in 2016.
He has scored 13 goals in 25 games for the Cityzens and is confident of winning the Premier League this term.
“I must honestly say that I can imagine that happening,” Gundogan told Sky Sport in Germany regarding whether he could see out the remainder of his playing days at City.
“The way they work here, not only athletically but also in all areas around it, is something I have never seen before in my career. I feel like the club is more than just the football itself and it’s just a nice feeling to be a part of this family.”
He added: “I think that in my career I have had phases in the past where I was playing just as well. The way I played football. Of course, what is added this season are the goals. The numbers are much better, that’s why it stands out even more at the moment.
“But that’s also because I play a more attacking role. I have more freedom when it comes to attacking the opposing goal. But also the hard work I do. I try to do everything as well as possible and take the best possible care of myself.”