Silva has two years left on his current deal, but will put pen to paper on a new five-year contract worth almost £200,000 a week, says the Daily Star.
City officials met his advisers in Spain last week while Silva was busy helping his country win Euro 2012 and he is set to sign in the next few days.
"I'm grateful for my experience at City and I have improved as a player, in every sense, since I joined them. I didn't know if I was capable of playing like this when I left Valencia.
"I'm on holiday right now, but my agents are negotiating a new deal with City and I think it's likely we close it in a very short time."