The Spain international joined City from Valencia in 2010, but has been regularly linked with a return to La Liga amid speculation Barcelona hold an interest in him.
Silva, though, is not concerned by the rumours and is determined to help City win a second Premier League title this season before targeting success in the Champions League.
"I'm very used to the rumours every summer," said Silva. "They have been around a long time.
"It's the way football works, just rumours. I'm very happy at Manchester City and I think that shows on the pitch as well.
"The first thing is that I want to win the Premier League this year. And then I want to win the Champions League. We want to get bigger every year, regardless of what is happening at Manchester United.
"I think this is the most exciting City team I have played in. That attacking style helps, not just for me, but for all the players to go forward and score more goals.
"I ask myself in every game to be the one to take responsibility. I enjoy creating goals more than scoring them."
City face local rivals United on Tuesday and know victory at Old Trafford will move Manuel Pellegrini's side to within three points of leaders Chelsea, with two games still in hand.
Silva will come up against Juan Mata again after the two players spent three years together at Valencia and the City playmaker is confident his old team-mate will eventually be a success after a stuttering start to his United career following his January move from Chelsea.
"It's a very difficult situation because the team is not playing that well," added Silva.
"They have not managed to bring the best out of him, but he's a very talented player, and he will show it. I know him very well. We played together many years. He's also a great guy and I'm sure it will work out for him.
"He wasn't having the minutes at Chelsea, so it was a good move for him, going to United to play."
Silva is also predicting a bright future for his compatriot David de Gea, who joined United from Atletico Madrid nearly three years ago.
He continued: "I wish David de Gea the best, obviously. He had a very difficult first year at United.
"I don't know him that well on a personal level, but he's a fantastic goalkeeper and, hopefully, he will make it.
"He's young with very good conditions as a goalkeeper and I can see him becoming Spain's No.1"