The 35-year-old former Barcelona and Arsenal star has started only one game for City this season and he admits he has a fringe role.
“It is an amazing and exciting thing to be at a club that has such ambition,” he told the club’s official website.
“Of course I would like to play football every week but I understand how to handle these things.”
Sylvinho is targeting a coaching role at Eastlands when his playing career is over.
“I would definitely like to remain longer,” he added.
“The project to make this club one of the best in Europe and the world cannot be completed in six months or a year and I would like to be part of it for as long as possible.
“What really pleased me was finding how big this club was already and that everyone around it is working hard to make it even bigger.
“We have a lot of good players and an intelligent and good man in manager Mark Hughes but the key is to make sure the mentality in the dressing room is right.
“Every minute of the day in every week has to be geared towards thinking about winning three points in the next game.
“We need to make people believe that we can do that. It is very important. Mentality is very important. Whatever we are aiming for, be it, top four, top three or top two, it is going to be difficult but easier if the mentality is there.”