Silva lifted the Supercoppa Italiana after beating Inter Milan 2-1, but admitted greater aspirations this coming season.
"I am not joking when I say that this Milan team can win everything. We have already won one trophy, but there are still three prizes missing.
"AC Milan can win the Champions League, but so can teams like Barcelona, Real Madrid and Manchester United. We have a very strong team, though, and are more than just an outsider," Silva said to La Gazzetta dello Sport.
"We have already shown that we're the best in Italy with that comeback against Inter. I also want to win the Coppa Italia this term. You must always have the ambition to win if you play football."
AC Milan will begin their Serie A campaign by travellingto Cagliari on August 27.