Vicente del Bosque's men are aiming for a third straight European Championship and open their tournament against the Czech Republic on June 13.
Silva was limited to 24 Premier League appearances for Manchester City this season due to ankle and hamstring injuries.
But the 30-year-old said he was nearing full fitness and eyeing Spain's Group D opener.
"I'm fine," Silva said, via Marca.
"I hope to reach the first game. I'm not sure. The feelings I have are good."
Silva is a veteran of 96 international caps for Spain and understands why his nation are favourites to win a fourth European title.
He is also eyeing a century of caps, saying: "I am thrilled to be close to 100. I'm on 96.
"Reaching that figure would be very nice."