Both Milan clubs, Chelsea and Bayern Munich have all been linked with a move for the 25-year-old, who was believed to be growing restless with a lack of first-team football.
AC Milan, Inter, Chelsea and Champions League holder Bayern Munich have all been linked with the defender in recent weeks amid reports he is growing restless about his first-team prospects.
Richards, who joined City as a youngster from Oldham, was restricted to seven Premier League appearances last term and started the campaign on the sidelines due to an injury sustained playing for Great Britain at the Olympics.
Competition for places is fierce, but Richards is determined to be part of Manuel Pellegrini's plans rather than seek a move away.
"Manchester City is my club and I've never considered playing anywhere else," the 25-year-old told the club's official website.
"I think there has been speculation because I've got two years left on my contract and Pablo Zabaleta had a fantastic season. He's outstanding but that's what you expect at top teams - you expect competition. The season before we won the Premier League I had a good year, but now I'm just happy to be back fit.
"Last season was a bit of a nightmare with injuries. I picked up the ankle problem at the Olympics and came back from that and then tore my cartilage. The main thing is to be playing. I know there are a lot of games and I don't expect to play every game but the season we won the title me and Zaba rotated really well together so if we can do that this season I'll be happy."