By moving to the Etihad Stadium he has become a direct rival of Mourinho, who is attempting to make United a challenger to City in the race to win the Premier League.
Despite that, Silva was happy to lavish Mourinho with praise.
"Jose Mourinho is a coach who says a lot about Portuguese football, which gives a fantastic dimension to our football," he told A Bola.
"He's a person I respect a lot. I met him relatively recently at the airport, we greeted each other and talked for a while.
"He is a rival, obviously, and I want to beat him, but he is a person I respect a lot and for whom I have great admiration for everything he has achieved in football."
Silva also backed under-fire United centre-back Victor Lindelof, whom he played alongside for a time at Benfica.
Silva said: "I know Lindelof well because I was with him in my second year of juniors and in the B team of Benfica. He's a friend.
"Victor is a player with a lot of quality, who likes to have the ball. In the most defensive positions here in England, the adaptation takes longer because it is a very aggressive and tough football.
"I hope things go well for him because he's a great player and a person I admire a lot."