The Premier League leaders host Bayern Munich in their final Group A match on Wednesday, needing to beat the group winners and hoping second-placed Napoli fail to win at Villarreal in order to progress to the last 16.
Mancini has rated his side's chances of progressing at 30 percent but Silva is a lot more optimistic.
"Of course, we've got to do well in the Champions League and, well, we should aim to win it. Why not? I don't think that is out of the question," the Spaniard said in an interview with the competition's official magazine.
"We need to improve upon what we've achieved already and keep progressing as a team."
The probability is, however, that City will be competing for the Europa League instead as the teams who finish third in the groups go through to the last 32 of the continent's second-tier club competition.
"We should try to beat Bayern Munich and we should hope that Villarreal can do a good game against Naples," the Italian told a news conference.
"But also if we don't go through in the Champions League, our life continues - we play in the Europa League and we will try to win the Europa League; it won't change anything.
"We did everything, we did some mistakes probably in this group but this can happen."
City's domestic form has been at odds with their European results as the debutants have let nerves get the better of them on the big stage but they will seek to treat Bayern with the ruthlessness of Saturday's 5-1 win over Norwich City.
"Let us hope that Arjen's suffering is finally over and he can start playing for us from the start now," Heynckes told reporters.
