The 25-year-old has shot the Citizens to the top of the Premier League table, and starred in their destruction of arch-rivals Manchester United in a 6-1 win last Sunday.
As a result, according to reports in the Daily Mail, both Pep Guardiola and Jose Mourinho have cast their eyes on Silva, who moved from Valencia to Manchester for £24 million in the summer of 2010.
However, speaking to Cadena SER, the player himself admitted he was pleased with the links, but intended to stay at Manchester.
"Madrid and Barcelona are great teams, but I'm happy here and I would like to stay here for many years. My family are the same as me, we're happy. The people treat me really well and I'm very relaxed. I live in a very peaceful area, a small town," Silva said.
"The important thing is the team. We are playing well and we are leaders. At the end of the season we will be in the fight and maybe we'll win the title.
"It's like any other club. They are putting together a great team and we hope to be one of the biggest sides in Europe.
"They [City] were the team who pushed hardest for me. I didn't have to think about it becuase they were the only team to push so hard to sign me and I'm happy."
He also refuted the suggestion that Mourinho had previously rejected a move for himself previously, saying: "There are so many players. Some have more opportunities than others. I always had the chance to come here with a lot of confidence [placed in me] and that didn't depend on me at all."
Silva admitted he was surprised how quickly he adapted to football in England.
"I thought it was going to be harder but they have made it easy for me and I'm happy," he continued.
"The atmosphere has surprised me, the competition and the relaxed atmosphere from day to day is fundamental. The public don't come in to the training sessions and at the games they are very respectful."
The striker also gave an insight towards his thoughts after City's 6-1 win over Manchester United at Old Trafford, ahead of their League Cup game against Wolves.
"I am going to enjoy it a little but in the knowledge that we have a game on Wednesday," the Spaniard said.
"On the pitch it's each man for himself but I wish [De Gea] all the best because he is a great goalkeeper and I am sure he will do really well [at United]", he concluded.