Roberto Mancini's side have to beat Bayern Munich, who have already qualified as Group A winners, on Wednesday and hope Napoli drop points at Villarreal.
And Silva is confident they can get through what has been a rollercoaster group stage to book their place in the last 16, saying: "We need to improve upon what we've achieved already and keep progressing as a team. Of course, we've got to do well in the Champions League and, well, we should aim to win it. Why not?
The Spanish international added: "I don't think that is out of the question."
City's first foray into the Champions League got off to a bad start with a disappointing 1-1 draw at home to Napoli and then a defeat in Munich which was memorable for being the origin of the now long-running Carlos Tevez saga.
Home and away victories over Villarreal got them back on track, only for their loss in Naples to put their progression in jeopardy. And although Bayern have dropped only two points in five matches, the 25-year-old is confident Mancini's squad will be looking to beat the Germans.
Silva said their mentality had partly been forged by the FA Cup final victory last season, which ended a major trophy drought spanning four decades.
"It was a key season for us. We won our first trophy for 35 years and qualified for the Champions League, claiming a place among the best teams in Europe," he told the official Champions League magazine.
"We're up there with the elite now and this is enabling us to attract winners. These players know how to win, must win and accept nothing else.
"Winners don't believe in fate like others do. They simply cannot accept defeat. The UEFA Champions League is certainly where we want to be and the level we have been aiming for.""
Source: PA
Source: PA